Table of spherical codes

Maintained by Henry Cohn

This data is archived at https://hdl.handle.net/1721.1/153543. If you cite the table, please refer to that data set, not this web page.

A spherical code is a configuration of points on the surface of a sphere, with the goal of maximizing the minimal angle between the points. The following table lists numerically optimized codes, with cases that are known to be optimal marked with *. Each entry links to coordinates for the code. Along with references, in some cases the table lists the minimal polynomial of the cosine of the minimal angle, in which case a code with this exact angle has been proved to exist.

The table is limited to 32 dimensions and 1024 points, with a few exceptions. It omits cases that have been systematically solved, namely dimensions below three and n-dimensional codes with at most 2n points (see R. A. Rankin, The closest packing of spherical caps in n dimensions, Proc. Glasgow Math. Assoc. 2 (1955), 139–144, doi:10.1017/S2040618500033219). The entries labeled “needs more optimization” have not fully converged to a local optimum, while most of the others probably have. There are two records listed in Ericson and Zinoviev's book (Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001) that I have not included below: for 80 points in 7 dimensions, their construction describes only 78 points, and for 1024 points in 16 dimensions, I am unable to get their construction to work.

You can access a plain text table here, which includes some polynomials too large to fit below, and upload additions or improvements here.

Dimension Number of points Cosine of minimal angle References and notes
3 7* 0.210138312731 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944.
3⁢x3−9⁢x2−3⁢x+1
3 8* 0.261203874964 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944.
7⁢x2+2⁢x−1
3 9* 0.333333333334 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944.
3⁢x−1
3 10* 0.404394325217 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944; L. Danzer, Finite point-sets on S2 with minimum distance as large as possible, Discrete Math. 60 (1986), 3–66, doi:10.1016/0012-365X(86)90002-6.
7⁢x3−4⁢x2−2⁢x+1
3 11* 0.447213595500 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944; L. Danzer, Finite point-sets on S2 with minimum distance as large as possible, Discrete Math. 60 (1986), 3–66, doi:10.1016/0012-365X(86)90002-6.
5⁢x2−1
3 12* 0.447213595500 L. Fejes [Tóth], Über eine Abschätzung des kürzesten Abstandes zweier Punkte eines auf einer Kugelfläche liegenden Punktsystems, Jber. Deutsch. Math.-Verein. 53 (1943), 66–68.
5⁢x2−1
3 13* 0.542636486830 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944; O. R. Musin and A. S. Tarasov, The strong thirteen spheres problem, Discrete Comput. Geom. 48 (2012), 128–141, doi:10.1007/s00454-011-9392-2.
x8−24⁢x7−12⁢x6+8⁢x5+38⁢x4+24⁢x3−12⁢x2−8⁢x+1
3 14* 0.563950300361 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944; O. R. Musin and A. S. Tarasov, The Tammes problem for N=14, Exp. Math. 24 (2015), 460–468, doi:10.1080/10586458.2015.1022842.
4⁢x4−2⁢x3+3⁢x2−1
3 15 0.592605902926 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944; D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
13⁢x5−x4+6⁢x3+2⁢x2−3⁢x−1
3 16 0.612294616483 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944.
23⁢x6+6⁢x5+5⁢x4+4⁢x3−3⁢x2−2⁢x−1
3 17 0.628094415071 L. Danzer, Finite point-sets on S2 with minimum distance as large as possible, Discrete Math. 60 (1986), 3–66, doi:10.1016/0012-365X(86)90002-6.
4⁢x10−92⁢x9+24⁢x8+128⁢x7−58⁢x6−78⁢x5+35⁢x4+32⁢x3−4⁢x2−6⁢x−1
3 18 0.648695832224 T. Tarnai and Zs. Gáspár, Improved packing of equal circles on a sphere and rigidity of its graph, Math. Proc. Cambridge Philos. Soc. 93 (1983), 191–218, doi:10.1017/S0305004100060485.
216⁢x11+108⁢x10+118⁢x9+209⁢x8−100⁢x7−160⁢x6+40⁢x5+46⁢x4−20⁢x3−12⁢x2+2⁢x+1
3 19 0.673116887561 D. E. Lazić, V. Šenk, and I. Šeškar, Arrangements of points on a sphere which maximize the least distance, Bull. Appl. Math. (Technical University Budapest) 47 (1987), 7–21.
Minimal polynomial listed in plain text data
3 20 0.676477138130 B. L. van der Waerden, Punkte auf der Kugel. Drei Zusätze, Math. Ann. 125 (1952), 213–222, doi:10.1007/BF01343118.
21⁢x3−9⁢x2−5⁢x+1
3 21 0.699498431067 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 22 0.710306258580 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
Minimal polynomial listed in plain text data
3 23 0.722846984869 T. Tarnai and Zs. Gáspár, Arrangement of 23 points on a sphere (on a conjecture of R. M. Robinson), Proc. Roy. Soc. London Ser. A 433 (1991), 257–267, doi:10.1098/rspa.1991.0046.
3 24* 0.723078468334 R. M. Robinson, Arrangements of 24 points on a sphere, Math. Ann. 144 (1961), 17–48, doi:10.1007/BF01396539.
7⁢x3+x2−3⁢x−1
3 25 0.747398628578 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
Minimal polynomial listed in plain text data
3 26 0.754278177121 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
Minimal polynomial listed in plain text data
3 27 0.758389210777 T. Tarnai and Zs. Gáspár, Improved packing of equal circles on a sphere and rigidity of its graph, Math. Proc. Cambridge Philos. Soc. 93 (1983), 191–218, doi:10.1017/S0305004100060485.
Minimal polynomial listed in plain text data
3 28 0.773230262338 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 29 0.780281415949 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 30 0.781551875095 B. W. Clare and D. L. Kepert, The closest packing of equal circles on a sphere, Proc. Roy. Soc. London Ser. A 405 (1986), 329–344, doi:10.1098/rspa.1986.0056.
Minimal polynomial listed in plain text data
3 31 0.791118613299 J. Strohmajer, Über die Verteilung von Punkten auf der Kugel, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 6 (1963), 49–53.
Minimal polynomial listed in plain text data
3 32 0.793616614872 L. Danzer, Finite point-sets on S2 with minimum distance as large as possible, Discrete Math. 60 (1986), 3–66, doi:10.1016/0012-365X(86)90002-6.
Minimal polynomial listed in plain text data
3 33 0.806397613648 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 34 0.810984337204 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 35 0.815937771500 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 36 0.817248185290 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 37 0.824892480240 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 38 0.826583259422 E. Székely, Sur le problème de Tammes, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae 17 (1974), 157–175, http://annalesm.elte.hu/annales17-1974/Annales_1974_T-XVII.pdf.
363⁢x14+7685⁢x12+34299⁢x10−77139⁢x8+68985⁢x6−31833⁢x4+6561⁢x2−729
3 39 0.833991322411 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 40 0.837162072474 B. W. Clare and D. L. Kepert, The closest packing of equal circles on a sphere, Proc. Roy. Soc. London Ser. A 405 (1986), 329–344, doi:10.1098/rspa.1986.0056.
3 41 0.841236343029 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 42 0.843331551639 E. Székely, Sur le problème de Tammes, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae 17 (1974), 157–175, http://annalesm.elte.hu/annales17-1974/Annales_1974_T-XVII.pdf.
Minimal polynomial listed in plain text data
3 43 0.847208865437 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 44 0.848201378305 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 45 0.854249474082 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 46 0.857534166865 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 47 0.859122361410 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 48 0.859292295076 R. M. Robinson, Finite sets of points on a sphere with each nearest to five others, Math. Ann. 179 (1969), 296–318, doi:10.1007/BF01350775.
34⁢x5+15⁢x4−12⁢x3−14⁢x2−6⁢x−1
3 49 0.866691479049 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 50 0.868173209127 E. Székely, Sur le problème de Tammes, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae 17 (1974), 157–175, http://annalesm.elte.hu/annales17-1974/Annales_1974_T-XVII.pdf.
Minimal polynomial listed in plain text data
3 51 0.871484364931 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 52 0.872966708781 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
Minimal polynomial listed in plain text data
3 53 0.876189803956 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 54 0.877004306358 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 55 0.880785046525 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 56 0.881731578410 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 57 0.884363737604 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 58 0.886555745177 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 59 0.887855737148 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 60 0.889473567590 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 61 0.892008443283 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 62 0.893496850569 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; J. Buddenhagen and D. A. Kottwitz, Multiplicity and symmetry breaking in (conjectured) densest packings of congruent circles on a circle, undated manuscript.
3 63 0.895036180815 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 64 0.896988167538 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 65 0.898259108584 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 66 0.899195777484 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 67 0.901198227760 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 68 0.902856921522 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 69 0.903831506358 James Buddenhagen and D. A. Kottwitz, 1997.
3 70 0.905043036803 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 71 0.906396736776 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 72 0.906849285445 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 73 0.909571628656 James Buddenhagen and D. A. Kottwitz, 1997.
3 74 0.910532623502 D. A. Kottwitz, 1997.
3 75 0.911390904652 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 76 0.912633133084 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; J. Buddenhagen and D. A. Kottwitz, Multiplicity and symmetry breaking in (conjectured) densest packings of congruent circles on a circle, undated manuscript.
3 77 0.913536344688 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
3 78 0.914034438768 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 79 0.916195009441 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 80 0.916690360742 James Buddenhagen, 1997.
3 81 0.918117193791 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 82 0.919172412416 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 83 0.919937881756 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 84 0.920151698890 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 85 0.922004026342 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 86 0.922710627798 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 87 0.923567597265 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 88 0.924093912593 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 89 0.925099726146 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 90 0.926173483336 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 91 0.926844825210 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 92 0.927003416243 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 93 0.928418531906 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 94 0.928979461777 James Buddenhagen and D. A. Kottwitz, 1997.
3 95 0.929811497467 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 96 0.930285673249 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 97 0.931051674650 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 98 0.931239991046 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 99 0.932727363300 James Buddenhagen and D. A. Kottwitz, 1997.
3 100 0.933385128903 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 101 0.934025767057 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 102 0.934480088172 James Buddenhagen and D. A. Kottwitz, 1997.
3 103 0.935207723062 James Buddenhagen and D. A. Kottwitz, 1997.
3 104 0.935711381000 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 105 0.936434497689 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 106 0.937042014619 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 107 0.937517802204 James Buddenhagen and D. A. Kottwitz, 1997.
3 108 0.937862018289 James Buddenhagen and D. A. Kottwitz, 1997.
3 109 0.938798085650 James Buddenhagen and D. A. Kottwitz, 1997.
3 110 0.939026290863 James Buddenhagen and D. A. Kottwitz, 1997.
3 111 0.939729959842 Henry Cohn, 2024.
3 112 0.940339774660 James Buddenhagen and D. A. Kottwitz, 1997.
3 113 0.940847649045 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 114 0.941205445297 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 115 0.941916896842 James Buddenhagen and D. A. Kottwitz, 1997.
3 116 0.942351017116 James Buddenhagen and D. A. Kottwitz, 1997.
3 117 0.942866795114 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; J. Buddenhagen and D. A. Kottwitz, Multiplicity and symmetry breaking in (conjectured) densest packings of congruent circles on a circle, undated manuscript.
3 118 0.943283453359 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 119 0.943652307933 James Buddenhagen and D. A. Kottwitz, 1997.
3 120 0.943662307333 R. M. Robinson, Finite sets of points on a sphere with each nearest to five others, Math. Ann. 179 (1969), 296–318, doi:10.1007/BF01350775.
1364⁢x10+1230⁢x9−709⁢x8−1468⁢x7−688⁢x6+136⁢x5+286⁢x4+108⁢x3+4⁢x2−6⁢x−1
3 121 0.944678061273 Henry Cohn, 2024.
3 122 0.945086237318 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 123 0.945482265531 James Buddenhagen and D. A. Kottwitz, 1997.
3 124 0.945780154584 James Buddenhagen and D. A. Kottwitz, 1997.
3 125 0.946396812867 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 126 0.946752784732 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 127 0.947264465646 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 128 0.947573544865 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 129 0.947971561157 James Buddenhagen and D. A. Kottwitz, 1997.
3 130 0.948266309315 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 131 0.948765511183 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 132 0.948962593971 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 133 0.949572658198 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 134 0.949971678353 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 135 0.950317557456 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 136 0.950634777737 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 137 0.951024783277 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 138 0.951358398188 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 139 0.951683443186 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 140 0.951979740880 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 141 0.952385754295 Henry Cohn, 2025.
3 142 0.952693726748 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 143 0.952998670435 Henry Cohn, 2024.
3 144 0.953228409663 Henry Cohn, 2025.
3 145 0.953609890346 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 146 0.953890527065 Henry Cohn, 2024.
3 147 0.954232032048 Henry Cohn, 2024.
3 148 0.954536757950 Henry Cohn, 2025.
3 149 0.954857978400 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 150 0.955020893900 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 151 0.955409384784 Henry Cohn, 2024.
3 152 0.955652691422 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 153 0.955934479813 Henry Cohn, 2025.
3 154 0.956200715693 Henry Cohn, 2024.
3 155 0.956523743427 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 156 0.956672320428 Henry Cohn, 2024.
3 157 0.957096132346 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 158 0.957339288658 Henry Cohn, 2024.
3 159 0.957588843682 Henry Cohn, 2024.
3 160 0.957856569962 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 161 0.958127175342 Henry Cohn, 2024.
3 162 0.958288809704 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 163 0.958615566728 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 164 0.958889976688 Henry Cohn, 2024.
3 165 0.959124889495 Henry Cohn, 2024.
3 166 0.959323846675 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 167 0.959625833713 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 168 0.959759331314 Henry Cohn, 2025.
3 169 0.960021869084 Henry Cohn, 2025.
3 170 0.960117137568 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121 (see footnote 1).
3 171 0.960456738161 Henry Cohn, 2025.
3 172 0.960629559055 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 173 0.960986467408 Henry Cohn, 2025.
3 174 0.961153945452 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 175 0.961330724045 Henry Cohn, 2024.
3 176 0.961593582498 Henry Cohn, 2024.
3 177 0.961828786663 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 178 0.961965173662 Henry Cohn, 2024.
3 179 0.962096013263 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 180 0.962128794086 T. Tarnai, Packing of 180 equal circles on a sphere, Elem. Math. 38 (1983), 119–122, doi:10.5169/seals-37194.
Minimal polynomial listed in plain text data
3 181 0.962508969964 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 182 0.962801835015 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 183 0.962987455061 Henry Cohn, 2024.
3 184 0.963227493195 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 185 0.963400251151 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 186 0.963602302299 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 187 0.963858096099 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 188 0.964002261472 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 189 0.964190407206 Henry Cohn, 2024.
3 190 0.964292984546 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 191 0.964504935278 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 192 0.964585751396 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 193 0.964893730830 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 194 0.965083352280 Henry Cohn, 2024.
3 195 0.965251036900 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 196 0.965468021791 Henry Cohn, 2024.
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3 215 0.968453681521 Henry Cohn, 2024.
3 216 0.968596893733 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 217 0.968776493956 Henry Cohn, 2025.
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3 268 0.974543890479 Henry Cohn, 2024.
3 269 0.974603593005 Henry Cohn, 2024.
3 270 0.974616849625 T. Tarnai and Zs. Gáspár, Multi-symmetric close packings of equal spheres on the spherical surface, Acta Cryst. Sect. A 43 (1987), 612–616, doi:10.1107/S0108767387098842.
Minimal polynomial listed in plain text data
3 271 0.974808781632 Henry Cohn, 2024.
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3 282 0.975817103894 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
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3 299 0.977214468409 Henry Cohn, 2025.
3 300 0.977219217071 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 301 0.977392313268 Henry Cohn, 2024.
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3 360 0.980946761337 T. Tarnai and Zs. Gáspár, Multi-symmetric close packings of equal spheres on the spherical surface, Acta Cryst. Sect. A 43 (1987), 612–616, doi:10.1107/S0108767387098842.
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3 387 0.982346497568 Henry Cohn, 2024.
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3 389 0.982452801700 Henry Cohn, 2024.
3 390 0.982505534053 Henry Cohn, 2024.
3 391 0.982555955538 Henry Cohn, 2024.
3 392 0.982591195901 Henry Cohn, 2024.
3 393 0.982649357699 Henry Cohn, 2024.
3 394 0.982692375827 Henry Cohn, 2024.
3 395 0.982725465540 Henry Cohn, 2024.
3 396 0.982767271242 Henry Cohn, 2024.
3 397 0.982799147942 Henry Cohn, 2024.
3 398 0.982821049056 Henry Cohn, 2024.
3 399 0.982857394032 Henry Cohn, 2024.
3 400 0.982915172693 Henry Cohn, 2024.
3 401 0.982950664530 Henry Cohn, 2024.
3 402 0.982983355551 Henry Cohn, 2024.
3 403 0.983049964328 Henry Cohn, 2024.
3 404 0.983111162319 Henry Cohn, 2024.
3 405 0.983168565133 Henry Cohn, 2024.
3 406 0.983206265163 Henry Cohn, 2024.
3 407 0.983247933087 Henry Cohn, 2024.
3 408 0.983288123210 Henry Cohn, 2024.
3 409 0.983324857501 Henry Cohn, 2024.
3 410 0.983356947085 Henry Cohn, 2024.
3 411 0.983397760620 Henry Cohn, 2024.
3 412 0.983428600189 Henry Cohn, 2024.
3 413 0.983461427167 Henry Cohn, 2024.
3 414 0.983495155996 Henry Cohn, 2024.
3 415 0.983545319874 Henry Cohn, 2024.
3 416 0.983572356049 Henry Cohn, 2024.
3 417 0.983606629507 Henry Cohn, 2024.
3 418 0.983668285529 Henry Cohn, 2024.
3 419 0.983709311243 Henry Cohn, 2024.
3 420 0.983735772266 Henry Cohn, 2024.
3 421 0.983801876824 Henry Cohn, 2024.
3 422 0.983837084033 Henry Cohn, 2024.
3 423 0.983879327689 Henry Cohn, 2024.
3 424 0.983915009758 Henry Cohn, 2024.
3 425 0.983947724258 Henry Cohn, 2024.
3 426 0.983967656850 Henry Cohn, 2024.
3 427 0.984017759902 Henry Cohn, 2024.
3 428 0.984060532882 Henry Cohn, 2024.
3 429 0.984101619024 Henry Cohn, 2024.
3 430 0.984134891966 Henry Cohn, 2024.
3 431 0.984165514392 Henry Cohn, 2024.
3 432 0.984201636678 Henry Cohn, 2024.
3 433 0.984246511178 Henry Cohn, 2024.
3 434 0.984282456244 Henry Cohn, 2024.
3 435 0.984322511170 Henry Cohn, 2024.
3 436 0.984359381087 Henry Cohn, 2024.
3 437 0.984376596212 Henry Cohn, 2024.
3 438 0.984419779873 Henry Cohn, 2024.
3 439 0.984459277522 Henry Cohn, 2024.
3 440 0.984472421765 Henry Cohn, 2024.
3 441 0.984527980944 Henry Cohn, 2024.
3 442 0.984559589051 Henry Cohn, 2024.
3 443 0.984592266668 Henry Cohn, 2024.
3 444 0.984628415926 Henry Cohn, 2024.
3 445 0.984667372266 Henry Cohn, 2024.
3 446 0.984702068844 Henry Cohn, 2024.
3 447 0.984730509217 Henry Cohn, 2024.
3 448 0.984778913431 Henry Cohn, 2024.
3 449 0.984813716313 Henry Cohn, 2024.
3 450 0.984846922701 Henry Cohn, 2024.
3 451 0.984872959879 Henry Cohn, 2024.
3 452 0.984911000119 Henry Cohn, 2024.
3 453 0.984942286924 Henry Cohn, 2024.
3 454 0.984966631268 Henry Cohn, 2024.
3 455 0.984994478749 Henry Cohn, 2024.
3 456 0.985031017295 Henry Cohn, 2024.
3 457 0.985064695326 Henry Cohn, 2024.
3 458 0.985097884587 Henry Cohn, 2024.
3 459 0.985126768610 Henry Cohn, 2024.
3 460 0.985152936945 Henry Cohn, 2026.
3 461 0.985198380759 Henry Cohn, 2024.
3 462 0.985225068423 Henry Cohn, 2024.
3 463 0.985261648362 Henry Cohn, 2024.
3 464 0.985297019485 Henry Cohn, 2024.
3 465 0.985321750708 Henry Cohn, 2024.
3 466 0.985359897849 Henry Cohn, 2024.
3 467 0.985386081788 Henry Cohn, 2024.
3 468 0.985411837325 Henry Cohn, 2024.
3 469 0.985444627723 Henry Cohn, 2024.
3 470 0.985482640963 Henry Cohn, 2024.
3 471 0.985509915678 Henry Cohn, 2024.
3 472 0.985527599242 Henry Cohn, 2024.
3 473 0.985558412595 Henry Cohn, 2024.
3 474 0.985607101360 Henry Cohn, 2024.
3 475 0.985630320536 Henry Cohn, 2024.
3 476 0.985665218249 Henry Cohn, 2024.
3 477 0.985693505781 Henry Cohn, 2024.
3 478 0.985716117012 Henry Cohn, 2026.
3 479 0.985721775338 Henry Cohn, 2024.
3 480 0.985721861452 T. Tarnai and Zs. Gáspár, Multi-symmetric close packings of equal spheres on the spherical surface, Acta Cryst. Sect. A 43 (1987), 612–616, doi:10.1107/S0108767387098842.
3 481 0.985812248918 Henry Cohn, 2024.
3 482 0.985842699690 Henry Cohn, 2024.
3 483 0.985872483761 Henry Cohn, 2024.
3 484 0.985900122939 Henry Cohn, 2024.
3 485 0.985924698901 Henry Cohn, 2024.
3 486 0.985950768752 Henry Cohn, 2024.
3 487 0.985985004243 Henry Cohn, 2024.
3 488 0.986009149228 Henry Cohn, 2024.
3 489 0.986026483781 Henry Cohn, 2024.
3 490 0.986063292599 Henry Cohn, 2024.
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3 500 0.986349227234 Henry Cohn, 2024.
3 501 0.986372404028 Henry Cohn, 2024.
3 502 0.986403542281 Henry Cohn, 2024.
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3 506 0.986508558172 Henry Cohn, 2024.
3 507 0.986527855040 Henry Cohn, 2024.
3 508 0.986562688022 Henry Cohn, 2024.
3 510 0.986562950498 Henry Cohn, 2025.
3 511 0.986645870423 Henry Cohn, 2024.
3 512 0.986668364004 Henry Cohn, 2024.
3 513 0.986700077118 Henry Cohn, 2024.
3 514 0.986720532797 Henry Cohn, 2024.
3 515 0.986749064827 Henry Cohn, 2024.
3 516 0.986773903019 Henry Cohn, 2024.
3 517 0.986799492641 Henry Cohn, 2024.
3 518 0.986819754209 Henry Cohn, 2024.
3 519 0.986848175284 Henry Cohn, 2024.
3 520 0.986876145782 Henry Cohn, 2024.
3 521 0.986900278325 Henry Cohn, 2024.
3 522 0.986922575232 Henry Cohn, 2024.
3 523 0.986951778704 Henry Cohn, 2024.
3 524 0.986971561505 Henry Cohn, 2024.
3 525 0.986995199336 Henry Cohn, 2024.
3 526 0.987019236077 Henry Cohn, 2024.
3 527 0.987049033347 Henry Cohn, 2024.
3 528 0.987069504316 Henry Cohn, 2024.
3 529 0.987089590281 Henry Cohn, 2024.
3 530 0.987121524163 Henry Cohn, 2024.
3 531 0.987141738237 Henry Cohn, 2024.
3 532 0.987165596115 Henry Cohn, 2024.
3 533 0.987185368627 Henry Cohn, 2024.
3 534 0.987215557894 Henry Cohn, 2024.
3 535 0.987234674397 Henry Cohn, 2024.
3 536 0.987259191622 Henry Cohn, 2024.
3 537 0.987271183218 Henry Cohn, 2024.
3 538 0.987304975991 Henry Cohn, 2024.
3 539 0.987336486625 Henry Cohn, 2024.
3 540 0.987351430022 Henry Cohn, 2024.
3 541 0.987380165789 Henry Cohn, 2024.
3 542 0.987388996662 Henry Cohn, 2024.
3 543 0.987425682607 Henry Cohn, 2024.
3 544 0.987447704608 Henry Cohn, 2024.
3 545 0.987469058651 Henry Cohn, 2024.
3 546 0.987491594825 Henry Cohn, 2024.
3 547 0.987512470728 Henry Cohn, 2024.
3 548 0.987533400403 Henry Cohn, 2024.
3 549 0.987547178474 Henry Cohn, 2024.
3 550 0.987583836919 Henry Cohn, 2024.
3 551 0.987606449640 Henry Cohn, 2024.
3 552 0.987622742921 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 553 0.987648249263 Henry Cohn, 2024.
3 554 0.987670281304 Henry Cohn, 2024.
3 555 0.987693259384 Henry Cohn, 2024.
3 556 0.987718378190 Henry Cohn, 2024.
3 557 0.987735307385 Henry Cohn, 2024.
3 558 0.987761309685 Henry Cohn, 2024.
3 559 0.987786834005 Henry Cohn, 2024.
3 560 0.987804065628 Henry Cohn, 2024.
3 561 0.987825037070 Henry Cohn, 2024.
3 562 0.987842915448 Henry Cohn, 2024.
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3 566 0.987930679295 Henry Cohn, 2024.
3 567 0.987952567335 Henry Cohn, 2024.
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3 569 0.987994333054 Henry Cohn, 2024.
3 570 0.988010035988 Henry Cohn, 2024.
3 571 0.988036994032 Henry Cohn, 2024.
3 572 0.988045143812 Henry Cohn, 2025.
3 573 0.988071465154 Henry Cohn, 2024.
3 574 0.988099427052 Henry Cohn, 2024.
3 575 0.988116092887 Henry Cohn, 2024.
3 576 0.988134624929 Henry Cohn, 2024.
3 577 0.988155543378 Henry Cohn, 2024.
3 578 0.988175563350 Henry Cohn, 2024.
3 579 0.988199193100 Henry Cohn, 2024.
3 580 0.988214394071 Henry Cohn, 2024.
3 581 0.988236302808 Henry Cohn, 2024.
3 582 0.988258915209 Henry Cohn, 2024.
3 583 0.988278440743 Henry Cohn, 2024.
3 584 0.988296373611 Henry Cohn, 2024.
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3 586 0.988336136398 Henry Cohn, 2024.
3 587 0.988354165587 Henry Cohn, 2024.
3 588 0.988371988004 Henry Cohn, 2024.
3 589 0.988390327285 Henry Cohn, 2024.
3 590 0.988413417033 Henry Cohn, 2024.
3 591 0.988431548471 Henry Cohn, 2024.
3 592 0.988452036069 Henry Cohn, 2024.
3 593 0.988468804433 Henry Cohn, 2024.
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3 595 0.988509243514 Henry Cohn, 2024.
3 596 0.988527025270 Henry Cohn, 2024.
3 597 0.988546258113 Henry Cohn, 2024.
3 598 0.988563711650 Henry Cohn, 2024.
3 599 0.988581647683 Henry Cohn, 2024.
3 600 0.988601034993 Henry Cohn, 2024.
3 601 0.988621946438 Henry Cohn, 2024.
3 602 0.988641437112 Henry Cohn, 2024.
3 603 0.988656942485 Henry Cohn, 2024.
3 604 0.988675027867 Henry Cohn, 2024.
3 605 0.988700462515 Henry Cohn, 2024.
3 606 0.988712847782 Henry Cohn, 2024.
3 607 0.988727431487 Henry Cohn, 2024.
3 608 0.988756306926 Henry Cohn, 2024.
3 609 0.988760157529 Henry Cohn, 2024.
3 610 0.988792706244 Henry Cohn, 2024.
3 611 0.988803996797 Henry Cohn, 2024.
3 612 0.988822833992 Henry Cohn, 2024.
3 613 0.988842455232 Henry Cohn, 2024.
3 614 0.988857096430 Henry Cohn, 2024.
3 615 0.988875778474 Henry Cohn, 2024.
3 616 0.988892714835 Henry Cohn, 2024.
3 617 0.988912783824 Henry Cohn, 2024.
3 618 0.988927807992 Henry Cohn, 2024.
3 619 0.988948201134 Henry Cohn, 2025.
3 620 0.988948235960 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 621 0.988984109802 Henry Cohn, 2024.
3 622 0.989000876941 Henry Cohn, 2024.
3 623 0.989012818314 Henry Cohn, 2024.
3 624 0.989034528790 Henry Cohn, 2024.
3 625 0.989054157149 Henry Cohn, 2024.
3 626 0.989070144515 Henry Cohn, 2024.
3 627 0.989088135354 Henry Cohn, 2024.
3 628 0.989105386471 Henry Cohn, 2024.
3 629 0.989121123248 Henry Cohn, 2024.
3 630 0.989134691942 Henry Cohn, 2024.
3 631 0.989155822068 Henry Cohn, 2024.
3 632 0.989172993109 Henry Cohn, 2024.
3 633 0.989188471837 Henry Cohn, 2024.
3 634 0.989202420209 Henry Cohn, 2024.
3 635 0.989219790718 Henry Cohn, 2024.
3 636 0.989242196163 Henry Cohn, 2024.
3 637 0.989258990501 Henry Cohn, 2024.
3 638 0.989267204518 Henry Cohn, 2024.
3 639 0.989290088613 Henry Cohn, 2024.
3 640 0.989301986015 Henry Cohn, 2024.
3 641 0.989321411266 Henry Cohn, 2024.
3 642 0.989332573182 Henry Cohn, 2024.
3 643 0.989352773976 Henry Cohn, 2024.
3 644 0.989371069478 Henry Cohn, 2024.
3 645 0.989382485431 Henry Cohn, 2024.
3 646 0.989398690989 Henry Cohn, 2024.
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3 648 0.989433849301 Henry Cohn, 2024.
3 649 0.989453044562 Henry Cohn, 2024.
3 650 0.989463904615 Henry Cohn, 2024.
3 651 0.989485039605 Henry Cohn, 2024.
3 652 0.989500668198 Henry Cohn, 2024.
3 653 0.989517659733 Henry Cohn, 2024.
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3 655 0.989547002612 Henry Cohn, 2024.
3 656 0.989563787961 Henry Cohn, 2024.
3 657 0.989576352164 Henry Cohn, 2024.
3 658 0.989590441670 Henry Cohn, 2024.
3 659 0.989608602208 Henry Cohn, 2024.
3 660 0.989626363395 Henry Cohn, 2024.
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3 662 0.989658469367 Henry Cohn, 2024.
3 663 0.989668542979 Henry Cohn, 2024.
3 664 0.989681374062 Henry Cohn, 2024.
3 665 0.989702032269 Henry Cohn, 2024.
3 666 0.989717535361 Henry Cohn, 2024.
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3 669 0.989761473114 Henry Cohn, 2024.
3 670 0.989765777159 Henry Cohn, 2024.
3 671 0.989792890413 Henry Cohn, 2024.
3 672 0.989799643833 Henry Cohn, 2024.
3 673 0.989818330488 Henry Cohn, 2024.
3 674 0.989833722485 Henry Cohn, 2024.
3 675 0.989852452169 Henry Cohn, 2024.
3 676 0.989861529212 Henry Cohn, 2024.
3 678 0.989879779829 Henry Cohn, 2024.
3 679 0.989905728538 Henry Cohn, 2024.
3 680 0.989921085378 Henry Cohn, 2024.
3 681 0.989936920244 Henry Cohn, 2024.
3 682 0.989955559541 Henry Cohn, 2024.
3 683 0.989973015974 Henry Cohn, 2024.
3 684 0.989976827933 Henry Cohn, 2024.
3 685 0.990001449211 Henry Cohn, 2024.
3 686 0.990006418271 Henry Cohn, 2024.
3 687 0.990025982355 Henry Cohn, 2024.
3 688 0.990037853003 Henry Cohn, 2024.
3 689 0.990051064090 Henry Cohn, 2024.
3 692 0.990060116362 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 693 0.990108022437 Henry Cohn, 2024.
3 694 0.990123873541 Henry Cohn, 2024.
3 695 0.990138225464 Henry Cohn, 2024.
3 696 0.990144937712 Henry Cohn, 2024.
3 697 0.990164610569 Henry Cohn, 2024.
3 698 0.990178131415 Henry Cohn, 2024.
3 699 0.990196847589 Henry Cohn, 2024.
3 700 0.990204754056 Henry Cohn, 2024.
3 702 0.990207507930 Henry Cohn, 2025.
3 703 0.990246510087 Henry Cohn, 2024.
3 704 0.990264421603 Henry Cohn, 2024.
3 705 0.990275791331 Henry Cohn, 2024.
3 706 0.990290378683 Henry Cohn, 2024.
3 707 0.990307749113 Henry Cohn, 2024.
3 708 0.990313284691 Henry Cohn, 2024.
3 709 0.990331708341 Henry Cohn, 2024.
3 711 0.990345295659 Henry Cohn, 2024.
3 712 0.990368376224 Henry Cohn, 2024.
3 713 0.990383651488 Henry Cohn, 2024.
3 714 0.990391904853 Henry Cohn, 2024.
3 715 0.990408038650 Henry Cohn, 2024.
3 716 0.990424201178 Henry Cohn, 2024.
3 717 0.990437124471 Henry Cohn, 2024.
3 718 0.990448237688 Henry Cohn, 2024.
3 719 0.990461529899 Henry Cohn, 2024.
3 720 0.990474919274 Henry Cohn, 2024.
3 721 0.990491371173 Henry Cohn, 2024.
3 722 0.990499809958 Henry Cohn, 2024.
3 723 0.990516894560 Henry Cohn, 2024.
3 724 0.990532198847 Henry Cohn, 2024.
3 725 0.990534529638 Henry Cohn, 2024.
3 726 0.990553141663 Henry Cohn, 2024.
3 727 0.990566965324 Henry Cohn, 2024.
3 728 0.990571284239 Henry Cohn, 2024.
3 729 0.990587255137 Henry Cohn, 2024.
3 730 0.990603287439 Henry Cohn, 2024.
3 731 0.990612626443 Henry Cohn, 2024.
3 732 0.990621413211 Henry Cohn, 2025.
3 733 0.990643551144 Henry Cohn, 2024.
3 734 0.990660617632 Henry Cohn, 2024.
3 735 0.990668792728 Henry Cohn, 2024.
3 736 0.990681732803 Henry Cohn, 2024.
3 737 0.990695306177 Henry Cohn, 2024.
3 738 0.990704677084 Henry Cohn, 2024.
3 739 0.990713057195 Henry Cohn, 2024.
3 740 0.990728865941 Henry Cohn, 2024.
3 741 0.990742245221 Henry Cohn, 2024.
3 742 0.990755361153 Henry Cohn, 2024.
3 743 0.990770576230 Henry Cohn, 2024.
3 744 0.990780046428 Henry Cohn, 2024.
3 745 0.990791226838 Henry Cohn, 2024.
3 746 0.990807128963 Henry Cohn, 2024.
3 747 0.990816878553 Henry Cohn, 2024.
3 748 0.990830906878 Henry Cohn, 2024.
3 749 0.990838053202 Henry Cohn, 2024.
3 750 0.990847475915 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 751 0.990857663690 Henry Cohn, 2024.
3 752 0.990872395915 Henry Cohn, 2024.
3 753 0.990883514545 Henry Cohn, 2024.
3 754 0.990901296816 Henry Cohn, 2024.
3 755 0.990905033119 Henry Cohn, 2024.
3 756 0.990922227516 Henry Cohn, 2024.
3 757 0.990937812953 Henry Cohn, 2024.
3 758 0.990946005792 Henry Cohn, 2024.
3 759 0.990954743746 Henry Cohn, 2024.
3 760 0.990970877087 Henry Cohn, 2024.
3 761 0.990976123095 Henry Cohn, 2024.
3 762 0.990993252010 Henry Cohn, 2024.
3 763 0.991002546962 Henry Cohn, 2024.
3 764 0.991020776255 Henry Cohn, 2024.
3 765 0.991029933301 Henry Cohn, 2024.
3 766 0.991038039796 Henry Cohn, 2024.
3 767 0.991054850991 Henry Cohn, 2024.
3 768 0.991063858891 Henry Cohn, 2024.
3 769 0.991073054499 Henry Cohn, 2024.
3 770 0.991085755280 Henry Cohn, 2024.
3 771 0.991097098258 Henry Cohn, 2024.
3 772 0.991107834438 Henry Cohn, 2024.
3 773 0.991120324668 Henry Cohn, 2024.
3 774 0.991132071939 Henry Cohn, 2024.
3 775 0.991145898664 Henry Cohn, 2024.
3 776 0.991156697126 Henry Cohn, 2024.
3 777 0.991161697853 Henry Cohn, 2024.
3 778 0.991178514334 Henry Cohn, 2024.
3 779 0.991188403576 Henry Cohn, 2024.
3 780 0.991195467101 Henry Cohn, 2024.
3 781 0.991212495316 Henry Cohn, 2024.
3 782 0.991221877841 Henry Cohn, 2024.
3 783 0.991227432227 Henry Cohn, 2024.
3 784 0.991237581418 Henry Cohn, 2024.
3 785 0.991250704363 Henry Cohn, 2024.
3 786 0.991265609504 Henry Cohn, 2024.
3 787 0.991279737346 Henry Cohn, 2024.
3 788 0.991287959034 Henry Cohn, 2024.
3 789 0.991298474057 Henry Cohn, 2024.
3 790 0.991311108786 Henry Cohn, 2024.
3 791 0.991319397658 Henry Cohn, 2024.
3 792 0.991327970122 Henry Cohn, 2024.
3 793 0.991343095341 Henry Cohn, 2024.
3 794 0.991355598368 Henry Cohn, 2024.
3 795 0.991362648296 Henry Cohn, 2024.
3 796 0.991373620973 Henry Cohn, 2024.
3 797 0.991382382844 Henry Cohn, 2024.
3 798 0.991394391213 Henry Cohn, 2024.
3 799 0.991408093880 Henry Cohn, 2024.
3 800 0.991414851715 Henry Cohn, 2024.
3 801 0.991425603623 Henry Cohn, 2024.
3 802 0.991437819695 Henry Cohn, 2024.
3 803 0.991450003639 Henry Cohn, 2024.
3 804 0.991459924550 Henry Cohn, 2024.
3 805 0.991468080347 Henry Cohn, 2024.
3 806 0.991480017656 Henry Cohn, 2024.
3 807 0.991488929993 Henry Cohn, 2024.
3 808 0.991499472524 Henry Cohn, 2024.
3 809 0.991513039166 Henry Cohn, 2024.
3 810 0.991520665687 Henry Cohn, 2024.
3 811 0.991534887804 Henry Cohn, 2024.
3 812 0.991541771500 Henry Cohn, 2024.
3 813 0.991547822510 Henry Cohn, 2024.
3 814 0.991561861128 Henry Cohn, 2024.
3 815 0.991569264349 Henry Cohn, 2024.
3 816 0.991580342934 Henry Cohn, 2024.
3 817 0.991591011326 Henry Cohn, 2024.
3 818 0.991606217466 Henry Cohn, 2024.
3 819 0.991611831024 Henry Cohn, 2024.
3 820 0.991624044122 Henry Cohn, 2024.
3 821 0.991631483847 Henry Cohn, 2024.
3 822 0.991640340040 Henry Cohn, 2024.
3 823 0.991650165081 Henry Cohn, 2024.
3 824 0.991660076581 Henry Cohn, 2024.
3 825 0.991671265549 Henry Cohn, 2024.
3 826 0.991681742391 Henry Cohn, 2024.
3 827 0.991695448495 Henry Cohn, 2024.
3 828 0.991700756929 Henry Cohn, 2024.
3 829 0.991713398461 Henry Cohn, 2024.
3 830 0.991721621394 Henry Cohn, 2024.
3 831 0.991727218135 Henry Cohn, 2024.
3 832 0.991735674478 Henry Cohn, 2024.
3 833 0.991757657241 Henry Cohn, 2024.
3 834 0.991761234909 Henry Cohn, 2024.
3 835 0.991775366198 Henry Cohn, 2024.
3 836 0.991780274903 Henry Cohn, 2024.
3 837 0.991787929640 Henry Cohn, 2024.
3 838 0.991802634344 Henry Cohn, 2024.
3 840 0.991804916272 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 841 0.991829212367 Henry Cohn, 2024.
3 842 0.991840819373 Henry Cohn, 2024.
3 843 0.991847889329 Henry Cohn, 2024.
3 844 0.991857775147 Henry Cohn, 2024.
3 845 0.991863629186 Henry Cohn, 2024.
3 846 0.991878532857 Henry Cohn, 2025.
3 847 0.991886320624 Henry Cohn, 2025.
3 848 0.991897746584 Henry Cohn, 2025.
3 852 0.991904249523 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 853 0.991942749939 Henry Cohn, 2025.
3 854 0.991951631435 Henry Cohn, 2025.
3 855 0.991962531819 Henry Cohn, 2025.
3 856 0.991972423212 Henry Cohn, 2025.
3 857 0.991979003112 Henry Cohn, 2025.
3 858 0.991987713948 Henry Cohn, 2025.
3 860 0.992000324488 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 861 0.992015656329 Henry Cohn, 2025.
3 862 0.992022903669 Henry Cohn, 2025.
3 863 0.992039444605 Henry Cohn, 2025.
3 864 0.992045910827 Henry Cohn, 2025.
3 865 0.992052833787 Henry Cohn, 2025.
3 866 0.992064050508 Henry Cohn, 2025.
3 867 0.992072381754 Henry Cohn, 2025.
3 868 0.992080033785 Henry Cohn, 2025.
3 869 0.992091623959 Henry Cohn, 2025.
3 872 0.992098850920 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 873 0.992125985753 Henry Cohn, 2025.
3 874 0.992130666610 Henry Cohn, 2025.
3 875 0.992141194210 Henry Cohn, 2025.
3 876 0.992148880613 Henry Cohn, 2025.
3 877 0.992154329715 Henry Cohn, 2025.
3 878 0.992168861340 Henry Cohn, 2025.
3 879 0.992171243331 Henry Cohn, 2025.
3 880 0.992185909971 Henry Cohn, 2025.
3 881 0.992192486886 Henry Cohn, 2025.
3 882 0.992198371680 Henry Cohn, 2025.
3 883 0.992209993174 Henry Cohn, 2025.
3 884 0.992219699147 Henry Cohn, 2025.
3 885 0.992231709887 Henry Cohn, 2025.
3 886 0.992239057053 Henry Cohn, 2025.
3 887 0.992242382220 Henry Cohn, 2025.
3 888 0.992258876226 Henry Cohn, 2025.
3 889 0.992268087253 Henry Cohn, 2025.
3 890 0.992270692003 Henry Cohn, 2025.
3 891 0.992282908648 Henry Cohn, 2025.
3 892 0.992289973548 Henry Cohn, 2025.
3 893 0.992298164886 Henry Cohn, 2025.
3 894 0.992309459744 Henry Cohn, 2025.
3 895 0.992316358484 Henry Cohn, 2025.
3 896 0.992319789432 Henry Cohn, 2025.
3 897 0.992332110080 Henry Cohn, 2025.
3 898 0.992338696092 Henry Cohn, 2025.
3 899 0.992349829991 Henry Cohn, 2025.
3 900 0.992360793848 Henry Cohn, 2024.
3 901 0.992366538174 Henry Cohn, 2025.
3 902 0.992377854101 Henry Cohn, 2025.
3 903 0.992382061576 Henry Cohn, 2025.
3 904 0.992392816154 Henry Cohn, 2025.
3 905 0.992400631964 Henry Cohn, 2025.
3 906 0.992409191703 Henry Cohn, 2025.
3 907 0.992416883647 Henry Cohn, 2025.
3 908 0.992422545672 Henry Cohn, 2025.
3 909 0.992432062810 Henry Cohn, 2025.
3 910 0.992437123795 Henry Cohn, 2025.
3 911 0.992443166019 Henry Cohn, 2025.
3 912 0.992454600852 Henry Cohn, 2025.
3 913 0.992469933271 Henry Cohn, 2025.
3 914 0.992471207708 Henry Cohn, 2025.
3 915 0.992482565852 Henry Cohn, 2025.
3 916 0.992492188420 Henry Cohn, 2025.
3 917 0.992500203453 Henry Cohn, 2025.
3 918 0.992507205651 Henry Cohn, 2025.
3 919 0.992516908676 Henry Cohn, 2025.
3 920 0.992518345854 Henry Cohn, 2025.
3 921 0.992532122129 Henry Cohn, 2025.
3 922 0.992539673688 Henry Cohn, 2025.
3 923 0.992547647599 Henry Cohn, 2025.
3 924 0.992553990146 Henry Cohn, 2025.
3 925 0.992565731685 Henry Cohn, 2025.
3 926 0.992569938693 Henry Cohn, 2025.
3 927 0.992580946257 Henry Cohn, 2025.
3 928 0.992583930232 Henry Cohn, 2025.
3 929 0.992590355210 Henry Cohn, 2025.
3 930 0.992602765384 Henry Cohn, 2025.
3 931 0.992610375347 Henry Cohn, 2025.
3 932 0.992616284375 Henry Cohn, 2025.
3 933 0.992624602034 Henry Cohn, 2025.
3 934 0.992631107765 Henry Cohn, 2025.
3 935 0.992640679227 Henry Cohn, 2025.
3 936 0.992649034124 Henry Cohn, 2025.
3 937 0.992657820696 Henry Cohn, 2025.
3 938 0.992665682904 Henry Cohn, 2025.
3 939 0.992672947443 Henry Cohn, 2025.
3 940 0.992677739706 Henry Cohn, 2025.
3 941 0.992688089317 Henry Cohn, 2025.
3 942 0.992696579115 Henry Cohn, 2025.
3 943 0.992702546437 Henry Cohn, 2025.
3 944 0.992713697005 Henry Cohn, 2025.
3 945 0.992717631580 Henry Cohn, 2025.
3 946 0.992723034803 Henry Cohn, 2025.
3 947 0.992729250719 Henry Cohn, 2025.
3 948 0.992740223152 Henry Cohn, 2025.
3 950 0.992751947060 Henry Cohn, 2025.
3 951 0.992767541985 Henry Cohn, 2025.
3 952 0.992771438024 Henry Cohn, 2025.
3 953 0.992778258864 Henry Cohn, 2025.
3 954 0.992786191374 Henry Cohn, 2025.
3 955 0.992791727019 Henry Cohn, 2025.
3 956 0.992801093482 Henry Cohn, 2025.
3 957 0.992810004476 Henry Cohn, 2025.
3 958 0.992817667647 Henry Cohn, 2025.
3 959 0.992826125413 Henry Cohn, 2025.
3 960 0.992830967656 Henry Cohn, 2024.
3 961 0.992838773549 Henry Cohn, 2025.
3 962 0.992843794794 Henry Cohn, 2025.
3 963 0.992852425763 Henry Cohn, 2025.
3 964 0.992860398135 Henry Cohn, 2025.
3 965 0.992871354421 Henry Cohn, 2025.
3 966 0.992875386015 Henry Cohn, 2025.
3 967 0.992882714198 Henry Cohn, 2025.
3 968 0.992886923604 Henry Cohn, 2025.
3 969 0.992896341783 Henry Cohn, 2025.
3 970 0.992903243757 Henry Cohn, 2025.
3 971 0.992910234827 Henry Cohn, 2025.
3 972 0.992915598654 Henry Cohn, 2025.
3 974 0.992925603203 Henry Cohn, 2025.
3 975 0.992935839740 Henry Cohn, 2025.
3 976 0.992946637569 Henry Cohn, 2025.
3 977 0.992953433939 Henry Cohn, 2025.
3 978 0.992962810288 Henry Cohn, 2025.
3 979 0.992968433192 Henry Cohn, 2025.
3 980 0.992974636259 Henry Cohn, 2024.
3 981 0.992982747599 Henry Cohn, 2025.
3 982 0.992988090846 Henry Cohn, 2025.
3 983 0.992998353831 Henry Cohn, 2025.
3 984 0.993003417762 Henry Cohn, 2025.
3 985 0.993011691492 Henry Cohn, 2025.
3 986 0.993015554264 Henry Cohn, 2025.
3 988 0.993023719135 Henry Cohn, 2025.
3 989 0.993037184620 Henry Cohn, 2025.
3 990 0.993045751650 Henry Cohn, 2025.
3 991 0.993050187813 Henry Cohn, 2025.
3 992 0.993061792827 Henry Cohn, 2025.
3 993 0.993062803097 Henry Cohn, 2025.
3 994 0.993075914352 Henry Cohn, 2025.
3 995 0.993078560947 Henry Cohn, 2025.
3 996 0.993085371709 Henry Cohn, 2025.
3 997 0.993095368942 Henry Cohn, 2025.
3 998 0.993098230447 Henry Cohn, 2025.
3 999 0.993106913603 Henry Cohn, 2025.
3 1000 0.993111266855 Henry Cohn, 2025.
3 1001 0.993123068371 Henry Cohn, 2025.
3 1002 0.993125622347 Henry Cohn, 2025.
3 1003 0.993132170420 Henry Cohn, 2025.
3 1004 0.993141407134 Henry Cohn, 2025.
3 1005 0.993148911123 Henry Cohn, 2025.
3 1006 0.993152122720 Henry Cohn, 2025.
3 1008 0.993159005478 Henry Cohn, 2025.
3 1010 0.993176753480 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 1011 0.993185799668 Henry Cohn, 2025.
3 1012 0.993195967770 Henry Cohn, 2025.
3 1013 0.993202916215 Henry Cohn, 2025.
3 1014 0.993210002788 Henry Cohn, 2025.
3 1015 0.993213366518 Henry Cohn, 2025.
3 1016 0.993220747476 Henry Cohn, 2025.
3 1017 0.993224054059 Henry Cohn, 2025.
3 1018 0.993234793239 Henry Cohn, 2025.
3 1020 0.993235373238 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 1021 0.993256895835 Henry Cohn, 2025.
3 1022 0.993258630946 Henry Cohn, 2025.
3 1023 0.993269506578 Henry Cohn, 2025.
3 1024 0.993274985225 Henry Cohn, 2025.
4 9 0.162015199612 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
16⁢x3−16⁢x2−4⁢x+1
4 10* 0.166666666667 A. L. Mackay, The packing of three-dimensional spheres on the surface of a four-dimensional hypersphere, J. Phys. A 13 (1980), 3373–3379, doi:10.1088/0305-4470/13/11/011; C. Bachoc and F. Vallentin, Optimality and uniqueness of the (4,10,1/6) spherical code, J. Combin. Theory Ser. A 116 (2009), 195–204, doi:10.1016/j.jcta.2008.05.001.
6⁢x−1
4 11 0.230405563595 L. T. Wille, Close packing in curved space by simulated annealing, Journal of Physics A: Mathematical and General 20 (1987), L1211–L1218, doi:10.1088/0305-4470/20/17/014.
8⁢x3−12⁢x2−2⁢x+1
4 12 0.25 A. L. Mackay, The packing of three-dimensional spheres on the surface of a four-dimensional hypersphere, J. Phys. A 13 (1980), 3373–3379, doi:10.1088/0305-4470/13/11/011.
4⁢x−1
4 13 0.307295653982 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
5632⁢x9+9472⁢x8−3072⁢x7−5888⁢x6+544⁢x5+944⁢x4+152⁢x3−44⁢x2−14⁢x−1
4 14 0.319518594213 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
58⁢x7+174⁢x6+140⁢x5−16⁢x4−54⁢x3−10⁢x2+4⁢x+1
4 15 0.350992175946 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
36⁢x4−18⁢x3+10⁢x2−1
4 16 0.387628177123 A. L. Mackay, The packing of three-dimensional spheres on the surface of a four-dimensional hypersphere, J. Phys. A 13 (1980), 3373–3379, doi:10.1088/0305-4470/13/11/011.
256⁢x10+1024⁢x9+256⁢x8−1152⁢x7+160⁢x6+176⁢x5−144⁢x4+36⁢x3+37⁢x2−6⁢x−3
4 17 0.412259362694 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 18 0.422819414074 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
Minimal polynomial listed in plain text data
4 19 0.434258545911 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
3⁢x2+x−1
4 20 0.434258545911 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
3⁢x2+x−1
4 21 0.471380858508 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
16⁢x8−128⁢x7−64⁢x6+32⁢x5+72⁢x4+32⁢x3−16⁢x2−8⁢x+1
4 22 0.497884130844 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 23 0.5 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
2⁢x−1
4 24* 0.5 L. Schläfli, Theorie der vielfachen Kontinuität [1852], Denkschriften der Schweizerischen naturforschenden Gesellschaft, vol. 38, J. H. Graf, Bern, 1901; D. de Laat, N. Leijenhorst, and W. H. H. de Muinck Keizer, Optimality and uniqueness of the D4 root system, preprint, 2024, arXiv:2404.18794.
2⁢x−1
4 25 0.537316056656 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 26 0.540789617698 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
3392⁢x6+2112⁢x5−496⁢x4−656⁢x3−132⁢x2+6⁢x−1
4 27 0.557591351181 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
794⁢x5+393⁢x4−344⁢x3−82⁢x2+6⁢x+1
4 28 0.567338804075 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 29 0.573148530449 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
Minimal polynomial listed in plain text data
4 30 0.584232813931 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 31 0.590765838581 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
4 32 0.595720149236 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 33 0.600755407756 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 34 0.610128556790 Henry Cohn, 2024.
4 35 0.621523986641 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 36 0.628309089475 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 37 0.630368722499 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 38 0.640732732793 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 39 0.646928247960 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 40 0.650497801063 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
4 41 0.655274051124 Henry Cohn, 2024.
4 42 0.658420878517 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 43 0.662667198430 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 44 0.668804906276 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
36⁢x8−60⁢x7+481⁢x6+166⁢x5−205⁢x4−116⁢x3+11⁢x2+10⁢x+1
4 45 0.676924957837 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 46 0.682325866078 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 47 0.685400852293 Henry Cohn, 2025.
4 48 0.689831186714 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 49 0.693413660571 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 50 0.693726127145 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
Minimal polynomial listed in plain text data
4 51 0.701375493264 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 52 0.703627792371 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 53 0.707671488219 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 54 0.709714380727 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 55 0.715661893754 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 56 0.719201427062 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 57 0.722366203194 Henry Cohn, 2025.
4 58 0.724963759986 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 59 0.726684594037 Henry Cohn, 2025.
4 60 0.728768479335 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 61 0.731517689032 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 62 0.733882910506 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 63 0.738725371284 Henry Cohn, 2025.
4 64 0.739558032728 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 65 0.742483255369 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 66 0.745996162085 Henry Cohn, 2025.
4 67 0.748966563154 Henry Cohn, 2025.
4 68 0.751044149551 Henry Cohn, 2025.
4 69 0.752628993819 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 70 0.753734038368 Henry Cohn, 2025.
4 71 0.756373364760 Henry Cohn, 2025.
4 72 0.758022144348 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 73 0.759191014470 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 74 0.759545691353 Henry Cohn, 2025.
4 75 0.760558878464 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 76 0.761064664765 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
Minimal polynomial listed in plain text data
4 77 0.765202546890 Henry Cohn, 2025.
4 78 0.768765601292 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 79 0.773060404397 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 80 0.775691894892 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 81 0.777799033764 Henry Cohn, 2025.
4 82 0.779753559198 Henry Cohn, 2025.
4 83 0.781053544402 Henry Cohn, 2025.
4 84 0.782373204314 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 85 0.783715044186 Henry Cohn, 2024.
4 86 0.784899018852 Henry Cohn, 2025.
4 87 0.785487328991 Henry Cohn, 2025.
4 88 0.785927649195 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 89 0.788520093069 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 90 0.790391197000 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 91 0.791393154383 Henry Cohn, 2025.
4 92 0.792211293351 Henry Cohn, 2025.
4 93 0.793047017514 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 94 0.793553793569 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 95 0.796982807052 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 96 0.797980534415 Henry Cohn, 2025.
4 97 0.799480375605 Henry Cohn, 2023.
4 98 0.800765983579 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 99 0.801793100994 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 100 0.803178722499 Henry Cohn, 2025.
4 101 0.803884649087 Henry Cohn, 2025.
4 102 0.804699654814 Henry Cohn, 2025.
4 103 0.805093331367 Henry Cohn, 2025.
4 104 0.806308735044 Henry Cohn, 2025.
4 105 0.807104890332 Henry Cohn, 2025.
4 106 0.807600771583 Henry Cohn, 2025.
4 107 0.808031793624 Henry Cohn, 2025.
4 108 0.808488610194 Henry Cohn, 2025.
4 109 0.808687291189 Henry Cohn, 2025.
4 110 0.808927278480 Henry Cohn, 2025.
4 111 0.808991157916 Henry Cohn, 2025.
4 112 0.809016055614 Henry Cohn, 2025.
4 113 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 114 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 115 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 116 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 117 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 118 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 119 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 120* 0.809016994375 L. Schläfli, Theorie der vielfachen Kontinuität [1852], Denkschriften der Schweizerischen naturforschenden Gesellschaft, vol. 38, J. H. Graf, Bern, 1901; K. Böröczky, Packing of spheres in spaces of constant curvature, Acta Mathematica Academiae Scientiarum Hungarica 32 (1978), 243–261, doi:10.1007/BF01902361.
4⁢x2−2⁢x−1
4 121 0.824638011670 Henry Cohn, 2025.
4 122 0.826371365501 Henry Cohn, 2025.
4 123 0.827331732524 Henry Cohn, 2025.
4 124 0.829076814196 Henry Cohn, 2025.
4 125 0.830275122838 Henry Cohn, 2025.
4 126 0.831265978577 Henry Cohn, 2025.
4 127 0.832258295757 Henry Cohn, 2025.
4 128 0.833179391366 Henry Cohn, 2025.
4 129 0.833853106202 Henry Cohn, 2025.
4 130 0.834729130389 Henry Cohn, 2025.
4 131 0.835454616797 Henry Cohn, 2025.
4 132 0.835826242592 Henry Cohn, 2025.
4 133 0.836970287069 Henry Cohn, 2025.
4 134 0.837549857120 Henry Cohn, 2025.
4 135 0.838174290974 Henry Cohn, 2025.
4 136 0.838408035762 Henry Cohn, 2025.
4 137 0.838792717376 Henry Cohn, 2025.
4 138 0.839094608099 Henry Cohn, 2025.
4 139 0.839507413737 Henry Cohn, 2024.
4 140 0.839796230234 Henry Cohn, 2025.
4 141 0.840152855333 Henry Cohn, 2024.
4 142 0.840928789319 Henry Cohn, 2025.
4 143 0.842625863066 Henry Cohn, 2025.
4 144 0.843251223216 Henry Cohn, 2025.
4 145 0.845004703395 Henry Cohn, 2025.
4 146 0.846045189902 Henry Cohn, 2024.
4 147 0.846906008500 Henry Cohn, 2025.
4 148 0.847320837337 Henry Cohn, 2025.
4 149 0.847701351395 Henry Cohn, 2025.
4 150 0.848008139501 Henry Cohn, 2025.
4 151 0.848395999617 Henry Cohn, 2025.
4 152 0.848746833410 Henry Cohn, 2024.
4 153 0.849106783811 Henry Cohn, 2025.
4 154 0.849448181031 Henry Cohn, 2024.
4 155 0.850528693851 Henry Cohn, 2025.
4 156 0.852364181174 Henry Cohn, 2025.
4 157 0.853098036527 Henry Cohn, 2025.
4 158 0.853541001367 Henry Cohn, 2025.
4 159 0.853851387665 Henry Cohn, 2025.
4 160 0.854015402705 Henry Cohn, 2025.
4 161 0.855036011488 Henry Cohn, 2025.
4 162 0.856011990176 Henry Cohn, 2025.
4 163 0.856498246684 Henry Cohn, 2025.
4 164 0.856668082967 Henry Cohn, 2025.
4 165 0.856908324217 Henry Cohn, 2024.
4 166 0.857225219240 Henry Cohn, 2025.
4 167 0.857623781724 Henry Cohn, 2025.
4 168 0.859313343133 Henry Cohn, 2025.
4 169 0.860417510162 Henry Cohn, 2025.
4 170 0.861336632417 Henry Cohn, 2026, needs more optimization.
4 171 0.861877205800 Henry Cohn, 2025.
4 172 0.862358805352 Henry Cohn, 2025.
4 173 0.862725307388 Henry Cohn, 2025.
4 174 0.863246308920 Henry Cohn, 2025.
4 175 0.863367463185 Henry Cohn, 2025.
4 176 0.863624102971 Henry Cohn, 2025.
4 177 0.863764381494 Henry Cohn, 2025.
4 178 0.863928834672 Henry Cohn, 2025.
4 179 0.864723195011 Henry Cohn, 2025.
4 180 0.865782670861 Henry Cohn, 2025.
4 181 0.866598382577 Henry Cohn, 2025.
4 182 0.867174335033 Henry Cohn, 2025.
4 183 0.867335807322 Henry Cohn, 2025.
4 184 0.867763055785 Henry Cohn, 2025.
4 185 0.868224155431 Henry Cohn, 2025.
4 186 0.868518800651 Henry Cohn, 2025.
4 187 0.868845310389 Henry Cohn, 2026, needs more optimization.
4 188 0.869207825431 Henry Cohn, 2025.
4 189 0.869491543071 Henry Cohn, 2025.
4 190 0.870050972636 Henry Cohn, 2025.
4 191 0.870814241870 Henry Cohn, 2025.
4 192 0.871341712847 Henry Cohn, 2025.
4 193 0.871545546243 Henry Cohn, 2025.
4 194 0.871792013221 Henry Cohn, 2025.
4 195 0.872106376131 Henry Cohn, 2025.
4 196 0.872623946731 Henry Cohn, 2025.
4 197 0.873487426793 Henry Cohn, 2025.
4 198 0.874156501901 Henry Cohn, 2025.
4 199 0.875069199577 Henry Cohn, 2025.
4 200 0.875686480655 Henry Cohn, 2025.
4 201 0.876308845876 Henry Cohn, 2025.
4 202 0.876662092953 Henry Cohn, 2025.
4 203 0.876862422683 Henry Cohn, 2026, needs more optimization.
4 204 0.877247713558 Henry Cohn, 2026, needs more optimization.
4 205 0.877534211883 Henry Cohn, 2025.
4 206 0.877831247728 Henry Cohn, 2025.
4 207 0.878017676728 Henry Cohn, 2025.
4 208 0.878215104089 Henry Cohn, 2025.
4 209 0.878616371731 Henry Cohn, 2025.
4 210 0.879213799752 Henry Cohn, 2025.
4 211 0.879586628106 Henry Cohn, 2025.
4 212 0.879665474531 Henry Cohn, 2025.
4 213 0.879834121318 Henry Cohn, 2025.
4 214 0.879945724274 Henry Cohn, 2025.
4 215 0.880272662054 Henry Cohn, 2025.
4 216 0.880905324150 Henry Cohn, 2025.
4 217 0.881535768813 Henry Cohn, 2025.
4 218 0.881833555267 Henry Cohn, 2025.
4 219 0.881957670465 Henry Cohn, 2025.
4 220 0.882547029792 Henry Cohn, 2025.
4 221 0.883034917637 Henry Cohn, 2025.
4 222 0.883456069925 Henry Cohn, 2025.
4 223 0.884138189446 Henry Cohn, 2025.
4 224 0.884684734191 Henry Cohn, 2025.
4 225 0.885143711620 Henry Cohn, 2026, needs more optimization.
4 226 0.885365198857 Henry Cohn, 2025.
4 227 0.885541386047 Henry Cohn, 2025.
4 228 0.885824040293 Henry Cohn, 2025.
4 229 0.886093486636 Henry Cohn, 2025.
4 230 0.886372063295 Henry Cohn, 2025.
4 231 0.886845140552 Henry Cohn, 2025.
4 232 0.887102089163 Henry Cohn, 2025.
4 233 0.887339463629 Henry Cohn, 2025.
4 234 0.887586535331 Henry Cohn, 2025.
4 235 0.887931434008 Henry Cohn, 2025.
4 236 0.888076450831 Henry Cohn, 2025.
4 237 0.888444553045 Henry Cohn, 2025.
4 238 0.888895172867 Henry Cohn, 2025.
4 239 0.889119578653 Henry Cohn, 2026, needs more optimization.
4 240 0.889506258287 Henry Cohn, 2025.
4 241 0.889886657931 Henry Cohn, 2025.
4 242 0.890234249504 Henry Cohn, 2025.
4 243 0.890327494714 Henry Cohn, 2025.
4 244 0.890767792098 Henry Cohn, 2025.
4 245 0.891024994652 Henry Cohn, 2025.
4 246 0.891230987587 Henry Cohn, 2025.
4 247 0.891768677571 Henry Cohn, 2025.
4 248 0.892111703446 Henry Cohn, 2025.
4 249 0.892307117218 Henry Cohn, 2026, needs more optimization.
4 250 0.892631521974 Henry Cohn, 2025.
4 251 0.893094674563 Henry Cohn, 2025.
4 252 0.893341841396 Henry Cohn, 2025.
4 253 0.893646236229 Henry Cohn, 2025.
4 254 0.893921970145 Henry Cohn, 2025.
4 255 0.894009501823 Henry Cohn, 2025.
4 256 0.894575161485 Henry Cohn, 2026, needs more optimization.
4 257 0.894967091737 Henry Cohn, 2026, needs more optimization.
4 258 0.895162078398 Henry Cohn, 2026, needs more optimization.
4 259 0.895560238243 Henry Cohn, 2026, needs more optimization.
4 260 0.895863531818 Henry Cohn, 2025, needs more optimization.
4 261 0.896074641602 Henry Cohn, 2026, needs more optimization.
4 262 0.896224478962 Henry Cohn, 2026, needs more optimization.
4 263 0.896411473848 Henry Cohn, 2026, needs more optimization.
4 264 0.896680909646 Henry Cohn, 2026, needs more optimization.
4 265 0.896868316981 Henry Cohn, 2026, needs more optimization.
4 266 0.897034498719 Henry Cohn, 2026, needs more optimization.
4 267 0.897247294157 Henry Cohn, 2026, needs more optimization.
4 268 0.897379521992 Henry Cohn, 2026, needs more optimization.
4 269 0.897716687703 Henry Cohn, 2026, needs more optimization.
4 270 0.897879064735 Henry Cohn, 2026, needs more optimization.
4 271 0.898149362730 Ilmari Vahteristo, 2026.
4 272 0.898273815183 Henry Cohn, 2025, needs more optimization.
4 273 0.898444364800 Henry Cohn, 2026, needs more optimization.
4 274 0.898527867663 Henry Cohn, 2025, needs more optimization.
4 275 0.898905582819 Henry Cohn, 2026, needs more optimization.
4 276 0.899228765953 Henry Cohn, 2026, needs more optimization.
4 277 0.899355536990 Henry Cohn, 2026, needs more optimization.
4 278 0.899522919658 Henry Cohn, 2026, needs more optimization.
4 279 0.899602410452 Henry Cohn, 2026, needs more optimization.
4 280 0.899645951104 Henry Cohn, 2026, needs more optimization.
4 281 0.900144251353 Henry Cohn, 2025, needs more optimization.
4 282 0.900669748687 Henry Cohn, 2025, needs more optimization.
4 283 0.901133860903 Henry Cohn, 2026, needs more optimization.
4 284 0.901400482679 Ilmari Vahteristo, 2026.
4 285 0.901725475267 Henry Cohn, 2026, needs more optimization.
4 286 0.902187173174 Henry Cohn, 2026, needs more optimization.
4 287 0.902238993011 Ilmari Vahteristo, 2026.
4 288 0.902809372927 Henry Cohn, 2025, needs more optimization.
4 289 0.902960715484 Henry Cohn, 2025, needs more optimization.
4 290 0.903114200287 Henry Cohn, 2026, needs more optimization.
4 291 0.903498175585 Henry Cohn, 2026, needs more optimization.
4 292 0.903643689020 Henry Cohn, 2025, needs more optimization.
4 293 0.903845491920 Henry Cohn, 2026, needs more optimization.
4 294 0.904174048251 Henry Cohn, 2025, needs more optimization.
4 295 0.904242053282 Henry Cohn, 2026, needs more optimization.
4 296 0.904791585539 Henry Cohn, 2026, needs more optimization.
4 297 0.904792565536 Henry Cohn, 2025, needs more optimization.
4 298 0.905081089280 Henry Cohn, 2026, needs more optimization.
4 299 0.905217873794 Henry Cohn, 2026, needs more optimization.
4 300 0.905430124030 Henry Cohn, 2026, needs more optimization.
4 301 0.905749679486 Henry Cohn, 2025, needs more optimization.
4 302 0.905981217126 Henry Cohn, 2026, needs more optimization.
4 303 0.906127796062 Henry Cohn, 2025, needs more optimization.
4 304 0.906270018142 Henry Cohn, 2026, needs more optimization.
4 305 0.906402554620 Henry Cohn, 2025, needs more optimization.
4 306 0.906574109379 Henry Cohn, 2026, needs more optimization.
4 307 0.907315489853 Henry Cohn, 2026, needs more optimization.
4 308 0.907321467879 Henry Cohn, 2026, needs more optimization.
4 309 0.907355948835 Henry Cohn, 2025, needs more optimization.
4 310 0.907358532815 Henry Cohn, 2025, needs more optimization.
4 311 0.907939119141 Henry Cohn, 2025, needs more optimization.
4 312 0.908400731703 Henry Cohn, 2026, needs more optimization.
4 313 0.908532014357 Henry Cohn, 2025, needs more optimization.
4 314 0.908551774846 Henry Cohn, 2025, needs more optimization.
4 315 0.908688049416 Henry Cohn, 2025, needs more optimization.
4 316 0.909046196578 Henry Cohn, 2026, needs more optimization.
4 317 0.909046386562 Henry Cohn, 2026, needs more optimization.
4 318 0.909170050134 Henry Cohn, 2025, needs more optimization.
4 319 0.909208466661 Henry Cohn, 2026, needs more optimization.
4 320 0.909390987337 Henry Cohn, 2026, needs more optimization.
4 321 0.909536185091 Henry Cohn, 2025, needs more optimization.
4 322 0.909674791274 Henry Cohn, 2025, needs more optimization.
4 323 0.909817307305 Henry Cohn, 2026, needs more optimization.
4 324 0.909901672991 Henry Cohn, 2025, needs more optimization.
4 325 0.910096010635 Henry Cohn, 2026, needs more optimization.
4 326 0.910283865043 Henry Cohn, 2025, needs more optimization.
4 327 0.910330672955 Henry Cohn, 2026, needs more optimization.
4 328 0.910660635640 Henry Cohn, 2025, needs more optimization.
4 329 0.910994704935 Henry Cohn, 2026, needs more optimization.
4 330 0.910999882705 Henry Cohn, 2025, needs more optimization.
4 331 0.911221815903 Henry Cohn, 2025, needs more optimization.
4 332 0.911382095911 Henry Cohn, 2026, needs more optimization.
4 333 0.911751408175 Henry Cohn, 2025, needs more optimization.
4 334 0.911800446547 Henry Cohn, 2026, needs more optimization.
4 335 0.912034339982 Henry Cohn, 2026, needs more optimization.
4 336 0.912308609413 Henry Cohn, 2025, needs more optimization.
4 337 0.912392820444 Henry Cohn, 2025, needs more optimization.
4 338 0.912655658852 Henry Cohn, 2026, needs more optimization.
4 339 0.913034799286 Henry Cohn, 2025, needs more optimization.
4 340 0.913196638557 Henry Cohn, 2026, needs more optimization.
4 341 0.913376620602 Henry Cohn, 2025, needs more optimization.
4 342 0.913523258748 Henry Cohn, 2024, needs more optimization.
4 343 0.914067345393 Henry Cohn, 2025, needs more optimization.
4 344 0.914230240004 Henry Cohn, 2025, needs more optimization.
4 345 0.914230519528 Henry Cohn, 2026, needs more optimization.
4 346 0.914438232359 Henry Cohn, 2025, needs more optimization.
4 347 0.914596841729 Henry Cohn, 2025, needs more optimization.
4 348 0.914781818832 Henry Cohn, 2026, needs more optimization.
4 349 0.914804715376 Henry Cohn, 2026, needs more optimization.
4 350 0.914972573951 Henry Cohn, 2025, needs more optimization.
4 351 0.915023495399 Henry Cohn, 2025, needs more optimization.
4 352 0.915307640705 Henry Cohn, 2026, needs more optimization.
4 353 0.915308989155 Henry Cohn, 2026, needs more optimization.
4 354 0.915475633531 Henry Cohn, 2026, needs more optimization.
4 355 0.915634904761 Henry Cohn, 2026, needs more optimization.
4 356 0.915670324528 Henry Cohn, 2026, needs more optimization.
4 357 0.915928280372 Henry Cohn, 2025, needs more optimization.
4 358 0.916202241466 Henry Cohn, 2025, needs more optimization.
4 359 0.916222668672 Henry Cohn, 2025, needs more optimization.
4 360 0.916292806442 Henry Cohn, 2026, needs more optimization.
4 361 0.916301661938 Henry Cohn, 2026, needs more optimization.
4 362 0.916499604247 Henry Cohn, 2026, needs more optimization.
4 363 0.916672248429 Henry Cohn, 2026, needs more optimization.
4 364 0.916810410726 Henry Cohn, 2026, needs more optimization.
4 365 0.916962145964 Henry Cohn, 2025, needs more optimization.
4 366 0.917029402271 Henry Cohn, 2025, needs more optimization.
4 367 0.917162341741 Henry Cohn, 2026, needs more optimization.
4 368 0.917277717682 Henry Cohn, 2025, needs more optimization.
4 369 0.917436486429 Henry Cohn, 2025, needs more optimization.
4 370 0.917439410227 Henry Cohn, 2026, needs more optimization.
4 371 0.917493460397 Henry Cohn, 2026, needs more optimization.
4 372 0.917973672642 Henry Cohn, 2026, needs more optimization.
4 373 0.918344892501 Henry Cohn, 2025, needs more optimization.
4 374 0.918405787049 Henry Cohn, 2026, needs more optimization.
4 375 0.918525851963 Henry Cohn, 2025, needs more optimization.
4 376 0.918529375746 Henry Cohn, 2026, needs more optimization.
4 377 0.918729610703 Henry Cohn, 2026, needs more optimization.
4 378 0.918919301726 Henry Cohn, 2025, needs more optimization.
4 379 0.919068186270 Henry Cohn, 2026, needs more optimization.
4 380 0.919090573869 Henry Cohn, 2025, needs more optimization.
4 381 0.919163200278 Henry Cohn, 2025, needs more optimization.
4 382 0.919320720843 Henry Cohn, 2026, needs more optimization.
4 383 0.919322999212 Henry Cohn, 2026, needs more optimization.
4 384 0.919541420163 Henry Cohn, 2026, needs more optimization.
4 385 0.919548006821 Henry Cohn, 2025, needs more optimization.
4 386 0.919555554896 Henry Cohn, 2026, needs more optimization.
4 387 0.919585651527 Henry Cohn, 2026, needs more optimization.
4 388 0.919734128283 Henry Cohn, 2026, needs more optimization.
4 389 0.919756054809 Henry Cohn, 2026, needs more optimization.
4 390 0.920168261588 Henry Cohn, 2026, needs more optimization.
4 391 0.920444192104 Henry Cohn, 2025, needs more optimization.
4 392 0.920447271773 Henry Cohn, 2026, needs more optimization.
4 393 0.920560967687 Henry Cohn, 2026, needs more optimization.
4 394 0.920564400221 Henry Cohn, 2025, needs more optimization.
4 395 0.920801296768 Henry Cohn, 2025, needs more optimization.
4 396 0.921058152262 Henry Cohn, 2026, needs more optimization.
4 397 0.921058203494 Henry Cohn, 2025, needs more optimization.
4 398 0.921351647740 Henry Cohn, 2025, needs more optimization.
4 399 0.921415178392 Henry Cohn, 2025, needs more optimization.
4 400 0.921512874155 Henry Cohn, 2026, needs more optimization.
4 401 0.921560426099 Henry Cohn, 2025, needs more optimization.
4 402 0.921787828480 Henry Cohn, 2026, needs more optimization.
4 403 0.921822136637 Henry Cohn, 2025, needs more optimization.
4 404 0.921896678330 Henry Cohn, 2026, needs more optimization.
4 405 0.921904900277 Henry Cohn, 2025, needs more optimization.
4 406 0.921929943872 Henry Cohn, 2025, needs more optimization.
4 408 0.922090364752 Henry Cohn, 2025, needs more optimization.
4 409 0.923053481556 Henry Cohn, 2026, needs more optimization.
4 410 0.923058192608 Henry Cohn, 2025, needs more optimization.
4 411 0.923059884394 Henry Cohn, 2026, needs more optimization.
4 412 0.923150924629 Henry Cohn, 2026, needs more optimization.
4 413 0.923265302229 Henry Cohn, 2025, needs more optimization.
4 414 0.923265471415 Henry Cohn, 2025, needs more optimization.
4 415 0.923452958450 Henry Cohn, 2026, needs more optimization.
4 416 0.923491299599 Henry Cohn, 2026, needs more optimization.
4 417 0.924180211328 Henry Cohn, 2025, needs more optimization.
4 418 0.924202985128 Henry Cohn, 2025, needs more optimization.
4 419 0.924325560783 Henry Cohn, 2025, needs more optimization.
4 420 0.924347915909 Henry Cohn, 2026, needs more optimization.
4 421 0.924562571586 Henry Cohn, 2025, needs more optimization.
4 422 0.924882682111 Henry Cohn, 2025, needs more optimization.
4 423 0.924973774846 Henry Cohn, 2025, needs more optimization.
4 424 0.925179917088 Henry Cohn, 2026, needs more optimization.
4 425 0.925342369999 Henry Cohn, 2026, needs more optimization.
4 426 0.925371775974 Henry Cohn, 2025, needs more optimization.
4 427 0.925417074839 Henry Cohn, 2025, needs more optimization.
4 428 0.925532846743 Henry Cohn, 2026, needs more optimization.
4 429 0.925657954234 Henry Cohn, 2025, needs more optimization.
4 430 0.925727886792 Henry Cohn, 2026, needs more optimization.
4 431 0.925881192521 Henry Cohn, 2026, needs more optimization.
4 432 0.926039163350 Henry Cohn, 2025, needs more optimization.
4 433 0.926141893047 Henry Cohn, 2026, needs more optimization.
4 434 0.926412475868 Henry Cohn, 2025, needs more optimization.
4 435 0.926570585016 Henry Cohn, 2025, needs more optimization.
4 436 0.926701577204 Henry Cohn, 2026, needs more optimization.
4 438 0.926855073228 Henry Cohn, 2025, needs more optimization.
4 439 0.927093468249 Henry Cohn, 2025, needs more optimization.
4 440 0.927146484882 Henry Cohn, 2026, needs more optimization.
4 441 0.927270883244 Henry Cohn, 2025, needs more optimization.
4 442 0.927285220818 Henry Cohn, 2026, needs more optimization.
4 443 0.927377843541 Henry Cohn, 2025, needs more optimization.
4 444 0.927438233419 Henry Cohn, 2026, needs more optimization.
4 445 0.927496635650 Henry Cohn, 2026, needs more optimization.
4 446 0.927688328376 Henry Cohn, 2025, needs more optimization.
4 447 0.927779601169 Henry Cohn, 2025, needs more optimization.
4 448 0.927913641653 Henry Cohn, 2025, needs more optimization.
4 449 0.928020259559 Henry Cohn, 2025, needs more optimization.
4 450 0.928076278877 Henry Cohn, 2025, needs more optimization.
4 451 0.928097969258 Henry Cohn, 2025, needs more optimization.
4 452 0.928193134829 Henry Cohn, 2026, needs more optimization.
4 453 0.928272948246 Henry Cohn, 2026, needs more optimization.
4 454 0.928373444080 Henry Cohn, 2025, needs more optimization.
4 455 0.928381173710 Henry Cohn, 2025, needs more optimization.
4 456 0.928554698947 Henry Cohn, 2025, needs more optimization.
4 457 0.928559891923 Henry Cohn, 2025, needs more optimization.
4 458 0.928714713007 Henry Cohn, 2025, needs more optimization.
4 459 0.928808529791 Henry Cohn, 2025, needs more optimization.
4 460 0.929058745508 Henry Cohn, 2025, needs more optimization.
4 461 0.929151290904 Henry Cohn, 2025, needs more optimization.
4 462 0.929180744654 Henry Cohn, 2025, needs more optimization.
4 463 0.929192297478 Henry Cohn, 2025, needs more optimization.
4 464 0.929307114423 Henry Cohn, 2026, needs more optimization.
4 465 0.929581795424 Henry Cohn, 2026, needs more optimization.
4 466 0.929681623171 Henry Cohn, 2026, needs more optimization.
4 467 0.929683139361 Henry Cohn, 2025, needs more optimization.
4 468 0.929790230602 Henry Cohn, 2026, needs more optimization.
4 469 0.929886943176 Henry Cohn, 2026, needs more optimization.
4 470 0.930044908339 Henry Cohn, 2025, needs more optimization.
4 471 0.930155433184 Henry Cohn, 2025, needs more optimization.
4 472 0.930304679917 Henry Cohn, 2026, needs more optimization.
4 473 0.930464634928 Henry Cohn, 2026, needs more optimization.
4 474 0.930640382606 Henry Cohn, 2026, needs more optimization.
4 475 0.930687865652 Henry Cohn, 2025, needs more optimization.
4 477 0.930820405012 Henry Cohn, 2025, needs more optimization.
4 478 0.930992801915 Henry Cohn, 2026, needs more optimization.
4 479 0.931005045840 Henry Cohn, 2026, needs more optimization.
4 480 0.931112380865 Henry Cohn, 2025, needs more optimization.
4 481 0.931335892594 Henry Cohn, 2025, needs more optimization.
4 482 0.931382412841 Henry Cohn, 2026, needs more optimization.
4 483 0.931486107590 Henry Cohn, 2026, needs more optimization.
4 484 0.931583863286 Henry Cohn, 2026, needs more optimization.
4 485 0.931598602760 Henry Cohn, 2025, needs more optimization.
4 486 0.931719293668 Henry Cohn, 2026, needs more optimization.
4 487 0.931837199002 Henry Cohn, 2025, needs more optimization.
4 488 0.931876606116 Henry Cohn, 2025, needs more optimization.
4 489 0.931879460145 Henry Cohn, 2025, needs more optimization.
4 490 0.931986511493 Henry Cohn, 2025, needs more optimization.
4 491 0.932129469048 Henry Cohn, 2025, needs more optimization.
4 492 0.932139733980 Henry Cohn, 2026, needs more optimization.
4 493 0.932233182674 Henry Cohn, 2026, needs more optimization.
4 494 0.932236467873 Henry Cohn, 2026, needs more optimization.
4 495 0.932323203465 Henry Cohn, 2025, needs more optimization.
4 496 0.932500272178 Henry Cohn, 2025, needs more optimization.
4 497 0.932512624213 Henry Cohn, 2025, needs more optimization.
4 498 0.932637534156 Henry Cohn, 2026, needs more optimization.
4 499 0.932641716231 Henry Cohn, 2025, needs more optimization.
4 500 0.932793878323 Henry Cohn, 2026, needs more optimization.
4 501 0.932795380893 Henry Cohn, 2025, needs more optimization.
4 502 0.932905617000 Henry Cohn, 2025, needs more optimization.
4 503 0.933005617030 Henry Cohn, 2025, needs more optimization.
4 504 0.933044432549 Henry Cohn, 2026, needs more optimization.
4 505 0.933128723647 Henry Cohn, 2025, needs more optimization.
4 506 0.933175916326 Henry Cohn, 2026, needs more optimization.
4 507 0.933399662810 Henry Cohn, 2026, needs more optimization.
4 508 0.933457715953 Henry Cohn, 2025, needs more optimization.
4 509 0.933553824747 Henry Cohn, 2025, needs more optimization.
4 510 0.933554354656 Henry Cohn, 2025, needs more optimization.
4 511 0.933747497746 Henry Cohn, 2026, needs more optimization.
4 512 0.933804302995 Henry Cohn, 2026, needs more optimization.
4 513 0.933898943863 Henry Cohn, 2026, needs more optimization.
4 514 0.933968668812 Henry Cohn, 2025, needs more optimization.
4 515 0.934045219268 Henry Cohn, 2025, needs more optimization.
4 516 0.934187930613 Henry Cohn, 2026, needs more optimization.
4 517 0.934200348230 Henry Cohn, 2026, needs more optimization.
4 518 0.934459599470 Henry Cohn, 2025, needs more optimization.
4 519 0.934540089409 Henry Cohn, 2025, needs more optimization.
4 520 0.934699248258 Henry Cohn, 2025, needs more optimization.
4 521 0.934710019106 Henry Cohn, 2025, needs more optimization.
4 522 0.934745753310 Henry Cohn, 2025, needs more optimization.
4 523 0.934852797622 Henry Cohn, 2026, needs more optimization.
4 524 0.934944371680 Henry Cohn, 2025, needs more optimization.
4 525 0.935029425094 Henry Cohn, 2026, needs more optimization.
4 526 0.935148024481 Henry Cohn, 2025, needs more optimization.
4 527 0.935256351959 Henry Cohn, 2025, needs more optimization.
4 528 0.935310315348 Henry Cohn, 2025, needs more optimization.
4 529 0.935319514565 Henry Cohn, 2026, needs more optimization.
4 530 0.935497863531 Henry Cohn, 2025, needs more optimization.
4 531 0.935510798794 Henry Cohn, 2025, needs more optimization.
4 532 0.935569232469 Henry Cohn, 2026, needs more optimization.
4 533 0.935676741118 Henry Cohn, 2025, needs more optimization.
4 534 0.935788386292 Henry Cohn, 2026, needs more optimization.
4 535 0.935811939995 Henry Cohn, 2025, needs more optimization.
4 537 0.935910089175 Henry Cohn, 2025, needs more optimization.
4 538 0.936073641293 Henry Cohn, 2025, needs more optimization.
4 539 0.936105500983 Henry Cohn, 2026, needs more optimization.
4 540 0.936187919569 Henry Cohn, 2026, needs more optimization.
4 541 0.936301405234 Henry Cohn, 2025, needs more optimization.
4 542 0.936307463358 Henry Cohn, 2025, needs more optimization.
4 543 0.936417878772 Henry Cohn, 2025, needs more optimization.
4 545 0.936558367404 Henry Cohn, 2025, needs more optimization.
4 546 0.936667874314 Henry Cohn, 2025, needs more optimization.
4 547 0.936744880456 Henry Cohn, 2026, needs more optimization.
4 548 0.936755768894 Henry Cohn, 2026, needs more optimization.
4 549 0.936916079422 Henry Cohn, 2025, needs more optimization.
4 550 0.936922956849 Henry Cohn, 2026, needs more optimization.
4 551 0.937084656947 Henry Cohn, 2026, needs more optimization.
4 552 0.937086856222 Henry Cohn, 2026, needs more optimization.
4 553 0.937240543392 Henry Cohn, 2025, needs more optimization.
4 554 0.937332328028 Henry Cohn, 2025, needs more optimization.
4 555 0.937361688429 Henry Cohn, 2025, needs more optimization.
4 556 0.937380785440 Henry Cohn, 2025, needs more optimization.
4 557 0.937468418241 Henry Cohn, 2025, needs more optimization.
4 558 0.937708798478 Henry Cohn, 2025, needs more optimization.
4 559 0.937710052202 Henry Cohn, 2025, needs more optimization.
4 560 0.937735092692 Henry Cohn, 2026, needs more optimization.
4 561 0.937829919092 Henry Cohn, 2026, needs more optimization.
4 562 0.937832503268 Henry Cohn, 2025, needs more optimization.
4 563 0.937955041395 Henry Cohn, 2025, needs more optimization.
4 564 0.937956581160 Henry Cohn, 2025, needs more optimization.
4 565 0.938152651024 Henry Cohn, 2025, needs more optimization.
4 566 0.938200710767 Henry Cohn, 2025, needs more optimization.
4 567 0.938202567350 Henry Cohn, 2025, needs more optimization.
4 568 0.938330431684 Henry Cohn, 2025, needs more optimization.
4 569 0.938356329917 Henry Cohn, 2026, needs more optimization.
4 570 0.938496721966 Henry Cohn, 2025, needs more optimization.
4 571 0.938513797968 Henry Cohn, 2025, needs more optimization.
4 572 0.938564289842 Henry Cohn, 2025, needs more optimization.
4 573 0.938764076152 Henry Cohn, 2025, needs more optimization.
4 574 0.938926625054 Henry Cohn, 2025, needs more optimization.
4 575 0.938934741529 Henry Cohn, 2025, needs more optimization.
4 576 0.939022786047 Henry Cohn, 2025, needs more optimization.
4 577 0.939023197122 Henry Cohn, 2025, needs more optimization.
4 578 0.939072946058 Henry Cohn, 2025, needs more optimization.
4 579 0.939148002539 Henry Cohn, 2025, needs more optimization.
4 580 0.939201274675 Henry Cohn, 2026, needs more optimization.
4 581 0.939214925124 Henry Cohn, 2026, needs more optimization.
4 582 0.939308245821 Henry Cohn, 2026, needs more optimization.
4 583 0.939358108278 Henry Cohn, 2025, needs more optimization.
4 584 0.939443313373 Henry Cohn, 2025, needs more optimization.
4 585 0.939460812797 Henry Cohn, 2025, needs more optimization.
4 586 0.939571319618 Henry Cohn, 2026, needs more optimization.
4 587 0.939573167768 Henry Cohn, 2026, needs more optimization.
4 588 0.939585867764 Henry Cohn, 2026, needs more optimization.
4 590 0.939702708834 Henry Cohn, 2025, needs more optimization.
4 592 0.939866827831 Henry Cohn, 2026, needs more optimization.
4 593 0.939871636807 Henry Cohn, 2026, needs more optimization.
4 594 0.939873198645 Henry Cohn, 2026, needs more optimization.
4 595 0.939983098032 Henry Cohn, 2026, needs more optimization.
4 596 0.939986602888 Henry Cohn, 2026, needs more optimization.
4 597 0.940099681249 Henry Cohn, 2025, needs more optimization.
4 598 0.940191207503 Henry Cohn, 2025, needs more optimization.
4 600 0.940371740470 Henry Cohn, 2025, needs more optimization.
4 601 0.940462666331 Henry Cohn, 2025, needs more optimization.
4 602 0.940524172905 Henry Cohn, 2025, needs more optimization.
4 603 0.940525601449 Henry Cohn, 2025, needs more optimization.
4 604 0.940582967501 Henry Cohn, 2026, needs more optimization.
4 605 0.940660094668 Henry Cohn, 2025, needs more optimization.
4 606 0.940662163379 Henry Cohn, 2025, needs more optimization.
4 607 0.940742759433 Henry Cohn, 2025, needs more optimization.
4 608 0.940825165665 Henry Cohn, 2026, needs more optimization.
4 609 0.940963167178 Henry Cohn, 2025, needs more optimization.
4 610 0.940986838892 Henry Cohn, 2025, needs more optimization.
4 611 0.941051663092 Henry Cohn, 2025, needs more optimization.
4 612 0.941115211625 Henry Cohn, 2025, needs more optimization.
4 613 0.941175083386 Henry Cohn, 2025, needs more optimization.
4 614 0.941194775682 Henry Cohn, 2026, needs more optimization.
4 615 0.941274274186 Henry Cohn, 2026, needs more optimization.
4 616 0.941285182477 Henry Cohn, 2025, needs more optimization.
4 617 0.941535461906 Henry Cohn, 2025, needs more optimization.
4 618 0.941538011697 Henry Cohn, 2025, needs more optimization.
4 619 0.941542102122 Henry Cohn, 2025, needs more optimization.
4 620 0.941642267240 Henry Cohn, 2025, needs more optimization.
4 621 0.941645219406 Henry Cohn, 2025, needs more optimization.
4 622 0.941698195844 Henry Cohn, 2025, needs more optimization.
4 623 0.941737504146 Henry Cohn, 2026, needs more optimization.
4 624 0.941798551676 Henry Cohn, 2026, needs more optimization.
4 625 0.941981654285 Henry Cohn, 2025, needs more optimization.
4 626 0.942000937392 Henry Cohn, 2025, needs more optimization.
4 627 0.942024040458 Henry Cohn, 2025, needs more optimization.
4 628 0.942134996678 Henry Cohn, 2025, needs more optimization.
4 629 0.942192328200 Henry Cohn, 2025, needs more optimization.
4 631 0.942363907789 Henry Cohn, 2025, needs more optimization.
4 632 0.942374827195 Henry Cohn, 2026, needs more optimization.
4 633 0.942473650646 Henry Cohn, 2025, needs more optimization.
4 634 0.942736605951 Henry Cohn, 2025, needs more optimization.
4 636 0.942737019308 Henry Cohn, 2025, needs more optimization.
4 637 0.942739881086 Henry Cohn, 2025, needs more optimization.
4 638 0.942777496521 Henry Cohn, 2025, needs more optimization.
4 639 0.942840895043 Henry Cohn, 2025, needs more optimization.
4 640 0.942921344577 Henry Cohn, 2026, needs more optimization.
4 641 0.943053199796 Henry Cohn, 2025, needs more optimization.
4 642 0.943076996937 Henry Cohn, 2026, needs more optimization.
4 643 0.943078020099 Henry Cohn, 2025, needs more optimization.
4 644 0.943180934082 Henry Cohn, 2025, needs more optimization.
4 645 0.943263346821 Henry Cohn, 2025, needs more optimization.
4 646 0.943264536655 Henry Cohn, 2025, needs more optimization.
4 647 0.943280433531 Henry Cohn, 2025, needs more optimization.
4 648 0.943291031540 Henry Cohn, 2025, needs more optimization.
4 649 0.943391411174 Henry Cohn, 2026, needs more optimization.
4 650 0.943396727354 Henry Cohn, 2026, needs more optimization.
4 651 0.943398346882 Henry Cohn, 2025, needs more optimization.
4 652 0.943420599120 Henry Cohn, 2026, needs more optimization.
4 653 0.943464499018 Henry Cohn, 2025, needs more optimization.
4 654 0.943482524163 Henry Cohn, 2025, needs more optimization.
4 655 0.943571235187 Henry Cohn, 2025, needs more optimization.
4 656 0.943573032589 Henry Cohn, 2026, needs more optimization.
4 657 0.943574218096 Henry Cohn, 2025, needs more optimization.
4 658 0.943601414683 Henry Cohn, 2025, needs more optimization.
4 659 0.943721696295 Henry Cohn, 2025, needs more optimization.
4 660 0.943757169743 Henry Cohn, 2026, needs more optimization.
4 661 0.943761106881 Henry Cohn, 2026, needs more optimization.
4 662 0.943765195886 Henry Cohn, 2025, needs more optimization.
4 664 0.943843773518 Henry Cohn, 2026, needs more optimization.
4 665 0.943851005572 Henry Cohn, 2025, needs more optimization.
4 666 0.943921780861 Henry Cohn, 2025, needs more optimization.
4 667 0.943923348839 Henry Cohn, 2025, needs more optimization.
4 668 0.943926024634 Henry Cohn, 2025, needs more optimization.
4 669 0.944000307055 Henry Cohn, 2025, needs more optimization.
4 670 0.944106517091 Henry Cohn, 2025, needs more optimization.
4 671 0.944118208019 Henry Cohn, 2025, needs more optimization.
4 672 0.944256472700 Henry Cohn, 2026, needs more optimization.
4 673 0.944357960966 Henry Cohn, 2025, needs more optimization.
4 674 0.944368205369 Henry Cohn, 2025, needs more optimization.
4 675 0.944537997000 Henry Cohn, 2025, needs more optimization.
4 676 0.944653424057 Henry Cohn, 2025, needs more optimization.
4 677 0.944654159692 Henry Cohn, 2026, needs more optimization.
4 679 0.944725392304 Henry Cohn, 2025, needs more optimization.
4 680 0.944745136087 Henry Cohn, 2025, needs more optimization.
4 681 0.944749674631 Henry Cohn, 2026, needs more optimization.
4 682 0.944859053848 Henry Cohn, 2026, needs more optimization.
4 683 0.944864452596 Henry Cohn, 2026, needs more optimization.
4 684 0.944933518727 Henry Cohn, 2025, needs more optimization.
4 685 0.944991182167 Henry Cohn, 2026, needs more optimization.
4 686 0.945085693951 Henry Cohn, 2025, needs more optimization.
4 687 0.945446050038 Henry Cohn, 2026, needs more optimization.
4 688 0.945446825922 Henry Cohn, 2026, needs more optimization.
4 689 0.945721674323 Henry Cohn, 2025, needs more optimization.
4 690 0.945777629919 Henry Cohn, 2026, needs more optimization.
4 691 0.945834751690 Henry Cohn, 2025, needs more optimization.
4 692 0.945892174743 Henry Cohn, 2026, needs more optimization.
4 693 0.945961558591 Henry Cohn, 2025, needs more optimization.
4 694 0.945971866588 Henry Cohn, 2026, needs more optimization.
4 695 0.946062307104 Henry Cohn, 2025, needs more optimization.
4 696 0.946064301813 Henry Cohn, 2026, needs more optimization.
4 697 0.946179220827 Henry Cohn, 2025, needs more optimization.
4 699 0.946181312763 Henry Cohn, 2025, needs more optimization.
4 700 0.946242389787 Henry Cohn, 2026, needs more optimization.
4 701 0.946313706669 Henry Cohn, 2025, needs more optimization.
4 702 0.946360743623 Henry Cohn, 2026, needs more optimization.
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4 704 0.946441318944 Henry Cohn, 2026, needs more optimization.
4 705 0.946448765341 Henry Cohn, 2025, needs more optimization.
4 706 0.946610192676 Henry Cohn, 2026, needs more optimization.
4 707 0.946622017817 Henry Cohn, 2026, needs more optimization.
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4 709 0.946724955645 Henry Cohn, 2025, needs more optimization.
4 711 0.946797578469 Henry Cohn, 2025, needs more optimization.
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4 716 0.946892530953 Henry Cohn, 2026, needs more optimization.
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4 718 0.946949775238 Henry Cohn, 2026, needs more optimization.
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4 720 0.947108699751 Henry Cohn, 2026, needs more optimization.
4 722 0.947155547724 Henry Cohn, 2026, needs more optimization.
4 723 0.947182737169 Henry Cohn, 2025, needs more optimization.
4 724 0.947240345492 Henry Cohn, 2026, needs more optimization.
4 726 0.947247520945 Henry Cohn, 2025, needs more optimization.
4 727 0.947393292682 Henry Cohn, 2025, needs more optimization.
4 728 0.947430437257 Henry Cohn, 2026, needs more optimization.
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4 733 0.947580880680 Henry Cohn, 2025, needs more optimization.
4 734 0.947587098177 Henry Cohn, 2025, needs more optimization.
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4 738 0.947819269951 Henry Cohn, 2026, needs more optimization.
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4 740 0.948007873107 Henry Cohn, 2026, needs more optimization.
4 742 0.948084008679 Henry Cohn, 2026, needs more optimization.
4 744 0.948106489674 Henry Cohn, 2026, needs more optimization.
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4 746 0.948222072640 Henry Cohn, 2025, needs more optimization.
4 747 0.948235644427 Henry Cohn, 2025, needs more optimization.
4 748 0.948396609258 Henry Cohn, 2026, needs more optimization.
4 750 0.948404264588 Henry Cohn, 2026, needs more optimization.
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4 752 0.948411007174 Henry Cohn, 2026, needs more optimization.
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4 754 0.948560623374 Henry Cohn, 2026, needs more optimization.
4 755 0.948601416034 Henry Cohn, 2026, needs more optimization.
4 756 0.948783172816 Henry Cohn, 2025, needs more optimization.
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4 758 0.948792950573 Henry Cohn, 2025, needs more optimization.
4 759 0.948822279577 Henry Cohn, 2025, needs more optimization.
4 760 0.948840430339 Henry Cohn, 2026, needs more optimization.
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4 763 0.948951196392 Henry Cohn, 2025, needs more optimization.
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4 765 0.949001397228 Henry Cohn, 2025, needs more optimization.
4 766 0.949174288632 Henry Cohn, 2026, needs more optimization.
4 768 0.949199812706 Henry Cohn, 2026, needs more optimization.
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4 770 0.949400655861 Henry Cohn, 2026, needs more optimization.
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4 772 0.949430772935 Henry Cohn, 2026, needs more optimization.
4 773 0.949433529396 Henry Cohn, 2026, needs more optimization.
4 774 0.949455425705 Henry Cohn, 2026, needs more optimization.
4 776 0.949519384499 Henry Cohn, 2026, needs more optimization.
4 778 0.949703143437 Henry Cohn, 2026, needs more optimization.
4 780 0.949732425293 Henry Cohn, 2026, needs more optimization.
4 781 0.949987000772 Henry Cohn, 2025, needs more optimization.
4 782 0.949988721320 Henry Cohn, 2025, needs more optimization.
4 788 0.949998985865 Henry Cohn, 2025, needs more optimization.
4 789 0.950008069781 Henry Cohn, 2025, needs more optimization.
4 790 0.950206068340 Henry Cohn, 2026, needs more optimization.
4 792 0.950243741902 Henry Cohn, 2026, needs more optimization.
4 794 0.950452996933 Henry Cohn, 2025, needs more optimization.
4 799 0.950456541411 Henry Cohn, 2025, needs more optimization.
4 802 0.950462877663 Henry Cohn, 2025, needs more optimization.
4 803 0.950465283823 Henry Cohn, 2025, needs more optimization.
4 816 0.950677458913 Henry Cohn, 2025, needs more optimization.
4 817 0.950788447617 Henry Cohn, 2026, needs more optimization.
4 818 0.950788817620 Henry Cohn, 2025, needs more optimization.
4 819 0.950790988511 Henry Cohn, 2026, needs more optimization.
4 840 0.950797547280 Henry Cohn, 2025, needs more optimization.
4 841 0.951651081876 Henry Cohn, 2026, needs more optimization.
4 842 0.951932284894 Henry Cohn, 2026, needs more optimization.
4 843 0.951950022478 Henry Cohn, 2026, needs more optimization.
4 844 0.951961649164 Henry Cohn, 2026, needs more optimization.
4 845 0.952192208755 Henry Cohn, 2025, needs more optimization.
4 847 0.952217603021 Henry Cohn, 2025, needs more optimization.
4 848 0.952218987686 Henry Cohn, 2025, needs more optimization.
4 849 0.952222127536 Henry Cohn, 2025, needs more optimization.
4 850 0.952239784851 Henry Cohn, 2025, needs more optimization.
4 851 0.952280860206 Henry Cohn, 2025, needs more optimization.
4 852 0.952284747198 Henry Cohn, 2026, needs more optimization.
4 853 0.952305685659 Henry Cohn, 2025, needs more optimization.
4 854 0.952385981186 Henry Cohn, 2026, needs more optimization.
4 856 0.952469970909 Henry Cohn, 2025, needs more optimization.
4 857 0.952471686698 Henry Cohn, 2025, needs more optimization.
4 858 0.952695248097 Henry Cohn, 2025, needs more optimization.
4 859 0.952698737895 Henry Cohn, 2026, needs more optimization.
4 860 0.952700137997 Henry Cohn, 2026, needs more optimization.
4 861 0.952763448969 Henry Cohn, 2025, needs more optimization.
4 862 0.952859748402 Henry Cohn, 2026, needs more optimization.
4 864 0.952876552024 Henry Cohn, 2026, needs more optimization.
4 866 0.952882242899 Henry Cohn, 2025, needs more optimization.
4 867 0.952902665462 Henry Cohn, 2025, needs more optimization.
4 868 0.952906611806 Henry Cohn, 2025, needs more optimization.
4 869 0.952918558454 Henry Cohn, 2025, needs more optimization.
4 872 0.953067626897 Henry Cohn, 2025, needs more optimization.
4 875 0.953104992009 Henry Cohn, 2025, needs more optimization.
4 876 0.953108610967 Henry Cohn, 2025, needs more optimization.
4 877 0.953110513304 Henry Cohn, 2025, needs more optimization.
4 878 0.953201275044 Henry Cohn, 2026, needs more optimization.
4 880 0.953473362023 Henry Cohn, 2025, needs more optimization.
4 881 0.953498792528 Henry Cohn, 2025, needs more optimization.
4 882 0.953511928838 Henry Cohn, 2026, needs more optimization.
4 883 0.953513789505 Henry Cohn, 2026, needs more optimization.
4 884 0.953525074998 Henry Cohn, 2025, needs more optimization.
4 885 0.953660979356 Henry Cohn, 2025, needs more optimization.
4 886 0.953669586269 Henry Cohn, 2025, needs more optimization.
4 887 0.953695413781 Henry Cohn, 2025, needs more optimization.
4 888 0.953700645565 Henry Cohn, 2026, needs more optimization.
4 889 0.953706262664 Henry Cohn, 2025, needs more optimization.
4 890 0.953717464100 Henry Cohn, 2025, needs more optimization.
4 891 0.953856705201 Henry Cohn, 2025, needs more optimization.
4 893 0.953864479437 Henry Cohn, 2025, needs more optimization.
4 894 0.953875593353 Henry Cohn, 2026, needs more optimization.
4 895 0.953876489808 Henry Cohn, 2025, needs more optimization.
4 896 0.953887694041 Henry Cohn, 2026, needs more optimization.
4 898 0.953936780784 Henry Cohn, 2026, needs more optimization.
4 900 0.954062876830 Henry Cohn, 2026, needs more optimization.
4 902 0.954068349973 Henry Cohn, 2025, needs more optimization.
4 904 0.954139878150 Henry Cohn, 2025, needs more optimization.
4 905 0.954145649734 Henry Cohn, 2025, needs more optimization.
4 906 0.954152636902 Henry Cohn, 2025, needs more optimization.
4 907 0.954160926763 Henry Cohn, 2025, needs more optimization.
4 908 0.954165607366 Henry Cohn, 2025, needs more optimization.
4 910 0.954196017446 Henry Cohn, 2026, needs more optimization.
4 911 0.954244205857 Henry Cohn, 2025, needs more optimization.
4 912 0.954332283926 Henry Cohn, 2026, needs more optimization.
4 913 0.954332978380 Henry Cohn, 2025, needs more optimization.
4 914 0.954361550477 Henry Cohn, 2026, needs more optimization.
4 915 0.954371201370 Henry Cohn, 2025, needs more optimization.
4 916 0.954372638011 Henry Cohn, 2025, needs more optimization.
4 917 0.954373815292 Henry Cohn, 2025, needs more optimization.
4 918 0.954377733468 Henry Cohn, 2025, needs more optimization.
4 919 0.954491745196 Henry Cohn, 2025, needs more optimization.
4 920 0.954544086173 Henry Cohn, 2026, needs more optimization.
4 921 0.954564180783 Henry Cohn, 2025, needs more optimization.
4 922 0.954633358317 Henry Cohn, 2026, needs more optimization.
4 923 0.954634824918 Henry Cohn, 2025, needs more optimization.
4 924 0.954806246462 Henry Cohn, 2025, needs more optimization.
4 925 0.954808607347 Henry Cohn, 2025, needs more optimization.
4 926 0.954811686442 Henry Cohn, 2025, needs more optimization.
4 927 0.954936284612 Henry Cohn, 2025, needs more optimization.
4 928 0.954936964671 Henry Cohn, 2026, needs more optimization.
4 929 0.954965530923 Henry Cohn, 2025, needs more optimization.
4 930 0.954992520001 Henry Cohn, 2025, needs more optimization.
4 931 0.955015118515 Henry Cohn, 2025, needs more optimization.
4 932 0.955021331426 Henry Cohn, 2025, needs more optimization.
4 933 0.955051675674 Henry Cohn, 2025, needs more optimization.
4 934 0.955113964488 Henry Cohn, 2026, needs more optimization.
4 936 0.955258943493 Henry Cohn, 2026, needs more optimization.
4 938 0.955261977602 Henry Cohn, 2026, needs more optimization.
4 940 0.955356743070 Henry Cohn, 2025, needs more optimization.
4 942 0.955384752051 Henry Cohn, 2026, needs more optimization.
4 943 0.955412046992 Henry Cohn, 2025, needs more optimization.
4 944 0.955626784466 Henry Cohn, 2026, needs more optimization.
4 946 0.955663730596 Henry Cohn, 2026, needs more optimization.
4 947 0.955740079345 Henry Cohn, 2025, needs more optimization.
4 948 0.955814638725 Henry Cohn, 2026, needs more optimization.
4 950 0.955818526127 Henry Cohn, 2026, needs more optimization.
4 951 0.955847659425 Henry Cohn, 2025, needs more optimization.
4 952 0.955901860381 Henry Cohn, 2026, needs more optimization.
4 953 0.955904646548 Henry Cohn, 2026, needs more optimization.
4 954 0.955908026022 Henry Cohn, 2026, needs more optimization.
4 955 0.955914337779 Henry Cohn, 2025, needs more optimization.
4 956 0.955914956613 Henry Cohn, 2026, needs more optimization.
4 957 0.955916742199 Henry Cohn, 2026, needs more optimization.
4 958 0.955931778657 Henry Cohn, 2026, needs more optimization.
4 960 0.955934538885 Henry Cohn, 2025, needs more optimization.
4 961 0.956011466695 Henry Cohn, 2026, needs more optimization.
4 962 0.956015541503 Henry Cohn, 2026, needs more optimization.
4 964 0.956100925104 Henry Cohn, 2026, needs more optimization.
4 966 0.956104990579 Henry Cohn, 2026, needs more optimization.
4 968 0.956155573662 Henry Cohn, 2026, needs more optimization.
4 970 0.956162959522 Henry Cohn, 2026, needs more optimization.
4 971 0.956192662084 Henry Cohn, 2025, needs more optimization.
4 972 0.956232654010 Henry Cohn, 2026, needs more optimization.
4 973 0.956331648598 Henry Cohn, 2025, needs more optimization.
4 974 0.956332591997 Henry Cohn, 2025, needs more optimization.
4 975 0.956340300559 Henry Cohn, 2025, needs more optimization.
4 976 0.956436399700 Henry Cohn, 2026, needs more optimization.
4 977 0.956436615854 Henry Cohn, 2025, needs more optimization.
4 978 0.956451283150 Henry Cohn, 2026, needs more optimization.
4 979 0.956490512655 Henry Cohn, 2025, needs more optimization.
4 980 0.956507243147 Henry Cohn, 2025, needs more optimization.
4 981 0.956578822561 Henry Cohn, 2025, needs more optimization.
4 982 0.956584248453 Henry Cohn, 2026, needs more optimization.
4 983 0.956655794511 Henry Cohn, 2025, needs more optimization.
4 984 0.956677294066 Henry Cohn, 2026, needs more optimization.
4 986 0.956684377189 Henry Cohn, 2026, needs more optimization.
4 987 0.956731139388 Henry Cohn, 2025, needs more optimization.
4 988 0.956859819250 Henry Cohn, 2026, needs more optimization.
4 989 0.956962111341 Henry Cohn, 2025, needs more optimization.
4 990 0.957090467119 Henry Cohn, 2026, needs more optimization.
4 991 0.957174095123 Henry Cohn, 2025, needs more optimization.
4 992 0.957233711366 Henry Cohn, 2026, needs more optimization.
4 994 0.957330300484 Henry Cohn, 2026, needs more optimization.
4 995 0.957468627778 Henry Cohn, 2026, needs more optimization.
4 997 0.957469247295 Henry Cohn, 2025, needs more optimization.
4 998 0.957621777801 Henry Cohn, 2025, needs more optimization.
4 999 0.957624065661 Henry Cohn, 2025, needs more optimization.
4 1000 0.957724044528 Henry Cohn, 2026, needs more optimization.
4 1001 0.957725518200 Henry Cohn, 2025, needs more optimization.
4 1002 0.957879169599 Henry Cohn, 2025, needs more optimization.
4 1003 0.957879722807 Henry Cohn, 2025, needs more optimization.
4 1004 0.957932175239 Henry Cohn, 2026, needs more optimization.
4 1005 0.957933585026 Henry Cohn, 2026, needs more optimization.
4 1006 0.958015395640 Henry Cohn, 2026, needs more optimization.
4 1007 0.958019677521 Henry Cohn, 2025, needs more optimization.
4 1008 0.958025392605 Henry Cohn, 2025, needs more optimization.
4 1009 0.958106506971 Henry Cohn, 2025, needs more optimization.
4 1010 0.958106563311 Henry Cohn, 2026, needs more optimization.
4 1011 0.958226168708 Henry Cohn, 2026, needs more optimization.
4 1012 0.958235111952 Henry Cohn, 2025, needs more optimization.
4 1013 0.958243797980 Henry Cohn, 2025, needs more optimization.
4 1014 0.958252619948 Henry Cohn, 2026, needs more optimization.
4 1015 0.958307571281 Henry Cohn, 2025, needs more optimization.
4 1016 0.958323656469 Henry Cohn, 2026, needs more optimization.
4 1017 0.958433314810 Henry Cohn, 2025, needs more optimization.
4 1018 0.958438216138 Henry Cohn, 2026, needs more optimization.
4 1019 0.958445105410 Henry Cohn, 2026, needs more optimization.
4 1020 0.958491952684 Henry Cohn, 2026, needs more optimization.
4 1021 0.958497806626 Henry Cohn, 2026, needs more optimization.
4 1023 0.958667893556 Henry Cohn, 2025, needs more optimization.
4 1024 0.958676090349 Henry Cohn, 2026, needs more optimization.
5 11 0.132853542599 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
45⁢x3−25⁢x2−5⁢x+1
5 12 0.153931605034 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
25⁢x4+30⁢x3+24⁢x2+2⁢x−1
5 13 0.187259851883 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
17⁢x3−5⁢x2−5⁢x+1
5 14 0.2 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
5⁢x−1
5 15 0.2 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
5⁢x−1
5 16* 0.2 T. Gosset, On the regular and semi-regular figures in space of n dimensions, Messenger Math. 29 (1900), 43–48; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
5⁢x−1
5 17 0.270475835269 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
9⁢x4−16⁢x3−10⁢x2+1
5 18 0.275501741660 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
484⁢x5−488⁢x4+97⁢x3+17⁢x2−x−1
5 19 0.291822399025 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
57⁢x6−38⁢x5−109⁢x4+32⁢x3+23⁢x2−10⁢x+1
5 20 0.299385692900 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
5⁢x3+13⁢x2−x−1
5 21 0.314916957176 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
Minimal polynomial listed in plain text data
5 22 0.354995034167 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 23 0.369772696944 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 24 0.374232982466 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
1620⁢x10+5508⁢x9−5751⁢x8−2406⁢x7+2055⁢x6+276⁢x5+559⁢x4−210⁢x3−127⁢x2+48⁢x−4
5 25 0.379621025394 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
5 26 0.390240659505 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
Minimal polynomial listed in plain text data
5 27 0.401659264277 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
5 28 0.408169699093 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 29 0.411034435092 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
Minimal polynomial listed in plain text data
5 30 0.413029776123 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
269⁢x7−1419⁢x6−283⁢x5+405⁢x4+15⁢x3−9⁢x2−x−1
5 31 0.433911863960 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
Minimal polynomial listed in plain text data
5 32 0.441830743928 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
8⁢x10−40⁢x9+74⁢x8−78⁢x7+73⁢x6−10⁢x5−3⁢x4+18⁢x3−9⁢x2−2⁢x+1
5 33 0.460004535963 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
5 34 0.470482910392 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 35 0.478437929066 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 36 0.483999000231 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
49⁢x6−6⁢x5−53⁢x4+12⁢x3+13⁢x2−2⁢x−1
5 37 0.493828518526 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 38 0.496243746648 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 39 0.499971927191 Henry Cohn, 2025.
5 40 0.5 A. Korkine and G. Zolotareff, Sur les formes quadratiques, Math. Ann. 6 (1873), 366–389, doi:10.1007/BF01442795; J. Leech, Five dimensional non-lattice sphere packings, Canad. Math. Bull. 10 (1967), 387–393, doi:10.4153/CMB-1967-037-5; F. Szöllősi, A note on five dimensional kissing arrangements, Math. Res. Lett. 30 (2023), no. 5, 1609–1615, doi:10.4310/MRL.2023.v30.n5.a13, arXiv:2301.08272; H. Cohn and I. Rajagopal, Variations on five-dimensional sphere packings, preprint, 2024, arXiv:2412.00937.
2⁢x−1
5 41 0.514994652513 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 42 0.518241155863 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 43 0.524709601830 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 44 0.527457712324 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 45 0.535068808289 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 46 0.538291308677 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 47 0.540668770936 Henry Cohn, 2025.
5 48 0.545112501822 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 49 0.546918160679 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
7⁢x2−2⁢x−1
5 50 0.546918160679 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x2−2⁢x−1
5 51 0.554740414282 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 52 0.560107395820 Henry Cohn, 2025.
5 53 0.566883217391 Henry Cohn, 2025.
5 54 0.571075948469 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 55 0.574604319465 Henry Cohn, 2025.
5 56 0.577211861101 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 57 0.577350269190 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3⁢x2−1
5 58 0.581466614772 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 59 0.586915485192 Henry Cohn, 2025.
5 60 0.593346597794 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 61 0.596251134208 Henry Cohn, 2025.
5 62 0.599005179291 Henry Cohn, 2023.
5 63 0.603554375176 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 64 0.605837370318 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 65 0.608465017856 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 66 0.608980005147 Henry Cohn, 2025.
5 67 0.611900403428 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 68 0.615240038880 Henry Cohn, 2025.
5 69 0.616793716634 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 70 0.617072261706 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 71 0.617972684614 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 72 0.617972684614 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 73 0.618033988750 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
x2+x−1
5 74 0.618033988750 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
x2+x−1
5 75 0.624659315083 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 76 0.631404527694 Henry Cohn, 2025.
5 77 0.636485570257 Henry Cohn, 2025.
5 78 0.640236043820 Henry Cohn, 2025.
5 79 0.643657523051 Henry Cohn, 2025.
5 80 0.646960184204 Henry Cohn, 2025.
5 81 0.648893901838 Henry Cohn, 2025.
5 82 0.651451517528 Henry Cohn, 2025.
5 83 0.655404165086 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 84 0.657612544747 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 85 0.659252981910 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 86 0.660931731561 Henry Cohn, 2025.
5 87 0.662618952049 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 88 0.664476994912 Henry Cohn, 2025.
5 89 0.666241382508 Henry Cohn, 2025.
5 90 0.666666666667 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
3⁢x−2
5 91 0.670415108805 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 92 0.672086633602 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 93 0.673830986224 Henry Cohn, 2025.
5 94 0.675154811372 Henry Cohn, 2025.
5 95 0.676048898306 Henry Cohn, 2026.
5 96 0.677473018556 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 97 0.679241845577 Henry Cohn, 2025.
5 98 0.680270697922 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 99 0.681881045310 Henry Cohn, 2025.
5 100 0.683153263764 Henry Cohn, 2025.
5 101 0.685186090412 Henry Cohn, 2025.
5 102 0.687443384073 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 103 0.688903541719 Henry Cohn, 2025.
5 104 0.689715870633 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 105 0.690713474104 Henry Cohn, 2025.
5 106 0.692005491905 Henry Cohn, 2025.
5 107 0.693863512900 Henry Cohn, 2025.
5 108 0.695352226010 Henry Cohn, 2025.
5 109 0.696434500115 Henry Cohn, 2025.
5 110 0.698102767792 Henry Cohn, 2025.
5 111 0.699314990430 Henry Cohn, 2025.
5 112 0.700443897808 Henry Cohn, 2025.
5 113 0.701786576995 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 114 0.703016293967 Henry Cohn, 2025.
5 115 0.704057149283 Henry Cohn, 2025.
5 116 0.705292505873 Henry Cohn, 2025.
5 117 0.706879377909 Henry Cohn, 2025.
5 118 0.708028481260 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 119 0.709336098101 Henry Cohn, 2025.
5 120 0.710406057156 Henry Cohn, 2025.
5 121 0.711530217808 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 122 0.712249276837 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 123 0.713918633096 Henry Cohn, 2025.
5 124 0.715099002544 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 125 0.716589774161 Henry Cohn, 2025.
5 126 0.717125378112 Henry Cohn, 2025.
5 127 0.718593652896 Henry Cohn, 2025.
5 128 0.719621301444 Henry Cohn, 2025.
5 129 0.720947646950 Henry Cohn, 2025.
5 130 0.721711816020 Henry Cohn, 2025.
5 131 0.723208608895 Henry Cohn, 2025.
5 132 0.724187141022 Henry Cohn, 2026, needs more optimization.
5 133 0.725096024568 Henry Cohn, 2026, needs more optimization.
5 134 0.726667487692 Henry Cohn, 2026, needs more optimization.
5 135 0.727819930944 Henry Cohn, 2025.
5 136 0.728641959070 Henry Cohn, 2026.
5 137 0.730011100633 Henry Cohn, 2025.
5 138 0.730143082796 Henry Cohn, 2025.
5 139 0.731013425800 Henry Cohn, 2026, needs more optimization.
5 140 0.731880138963 Henry Cohn, 2025.
5 141 0.732960070489 Henry Cohn, 2026, needs more optimization.
5 142 0.733688627543 Henry Cohn, 2025.
5 143 0.734506087652 Henry Cohn, 2025.
5 144 0.735189318066 Henry Cohn, 2025.
5 145 0.736519094966 Henry Cohn, 2025.
5 146 0.736648368146 Henry Cohn, 2025.
5 147 0.736967148066 Henry Cohn, 2025.
5 148 0.737200174837 Henry Cohn, 2025.
5 149 0.737884019958 Henry Cohn, 2025.
5 150 0.738295981996 Henry Cohn, 2025.
5 151 0.739521457056 Henry Cohn, 2026, needs more optimization.
5 152 0.739824519106 Henry Cohn, 2025.
5 153 0.740779971316 Henry Cohn, 2025.
5 154 0.741354012157 Henry Cohn, 2025.
5 155 0.742161234709 Henry Cohn, 2025.
5 156 0.742808811623 Henry Cohn, 2025.
5 157 0.743339290160 Henry Cohn, 2025.
5 158 0.743500742995 Henry Cohn, 2025.
5 159 0.743825044322 Henry Cohn, 2025.
5 160 0.744143092099 Henry Cohn, 2025.
5 161 0.747768123526 Henry Cohn, 2025.
5 162 0.748843925322 Henry Cohn, 2025.
5 163 0.750218552457 Henry Cohn, 2025.
5 164 0.750876806783 Henry Cohn, 2025.
5 165 0.752079878060 Henry Cohn, 2025.
5 166 0.752534073395 Henry Cohn, 2025.
5 167 0.753532673949 Henry Cohn, 2025.
5 168 0.754218675211 Henry Cohn, 2025.
5 169 0.755416175364 Henry Cohn, 2025.
5 170 0.755993792807 Henry Cohn, 2025.
5 171 0.756800051039 Henry Cohn, 2025.
5 172 0.757288355849 Henry Cohn, 2025.
5 173 0.758729438844 Henry Cohn, 2026, needs more optimization.
5 174 0.759690412033 Henry Cohn, 2025.
5 175 0.760597483271 Henry Cohn, 2025.
5 176 0.761278064091 Henry Cohn, 2025.
5 177 0.762581525327 Henry Cohn, 2026, needs more optimization.
5 178 0.763315108223 Henry Cohn, 2025.
5 179 0.764671222232 Henry Cohn, 2025.
5 180 0.764830852765 Henry Cohn, 2025.
5 181 0.764889493147 Henry Cohn, 2026, needs more optimization.
5 182 0.765464615641 Henry Cohn, 2026, needs more optimization.
5 183 0.765786900083 Henry Cohn, 2026, needs more optimization.
5 184 0.766400913097 Henry Cohn, 2026, needs more optimization.
5 185 0.766899697376 Henry Cohn, 2026, needs more optimization.
5 186 0.767756284641 Henry Cohn, 2026, needs more optimization.
5 187 0.768406152885 Henry Cohn, 2026, needs more optimization.
5 188 0.769144003907 Henry Cohn, 2026, needs more optimization.
5 189 0.769761315714 Henry Cohn, 2026, needs more optimization.
5 190 0.770220241203 Henry Cohn, 2025.
5 191 0.770477151449 Henry Cohn, 2025.
5 192 0.771178995101 Henry Cohn, 2026, needs more optimization.
5 193 0.771625226483 Henry Cohn, 2026, needs more optimization.
5 194 0.772357310102 Henry Cohn, 2025.
5 195 0.772914025091 Henry Cohn, 2025.
5 196 0.773820141713 Henry Cohn, 2025.
5 197 0.774290878773 Henry Cohn, 2025.
5 198 0.774958465360 Henry Cohn, 2026, needs more optimization.
5 199 0.775242540360 Henry Cohn, 2025.
5 200 0.775814258853 Henry Cohn, 2025.
5 201 0.776383781495 Henry Cohn, 2026, needs more optimization.
5 202 0.777028127031 Henry Cohn, 2026, needs more optimization.
5 203 0.777851537471 Henry Cohn, 2026, needs more optimization.
5 204 0.778262339953 Henry Cohn, 2025.
5 205 0.779048071982 Henry Cohn, 2025.
5 206 0.779408327452 Henry Cohn, 2026, needs more optimization.
5 207 0.780186249913 Henry Cohn, 2025.
5 208 0.780796988483 Henry Cohn, 2026, needs more optimization.
5 209 0.781333225832 Henry Cohn, 2025.
5 210 0.782396341668 Henry Cohn, 2026, needs more optimization.
5 211 0.782855932265 Henry Cohn, 2026, needs more optimization.
5 212 0.783016654957 Henry Cohn, 2025.
5 213 0.783762971528 Henry Cohn, 2026, needs more optimization.
5 214 0.784221920412 Henry Cohn, 2025.
5 215 0.784440391336 Henry Cohn, 2025.
5 216 0.785143218786 Henry Cohn, 2026, needs more optimization.
5 217 0.785510050827 Henry Cohn, 2025.
5 218 0.785996484357 Henry Cohn, 2025.
5 219 0.786769446899 Henry Cohn, 2026, needs more optimization.
5 220 0.787295059910 Henry Cohn, 2025.
5 221 0.787561403335 Henry Cohn, 2025.
5 222 0.788126323248 Henry Cohn, 2025.
5 223 0.788437486442 Henry Cohn, 2025.
5 224 0.788866206268 Henry Cohn, 2025.
5 225 0.789325624436 Henry Cohn, 2025.
5 226 0.789501827423 Henry Cohn, 2026, needs more optimization.
5 227 0.790566449848 Henry Cohn, 2025.
5 228 0.790672451290 Henry Cohn, 2026, needs more optimization.
5 229 0.790950228764 Henry Cohn, 2025.
5 230 0.791641402438 Henry Cohn, 2026, needs more optimization.
5 231 0.791859278921 Henry Cohn, 2025.
5 232 0.792500892930 Henry Cohn, 2025.
5 233 0.792671214420 Henry Cohn, 2026, needs more optimization.
5 234 0.792936161090 Henry Cohn, 2026, needs more optimization.
5 235 0.793680055721 Henry Cohn, 2025.
5 236 0.794236325882 Henry Cohn, 2025.
5 237 0.794670674646 Henry Cohn, 2025.
5 238 0.795014640201 Henry Cohn, 2025.
5 239 0.795425406950 Henry Cohn, 2025.
5 240 0.795938099707 Henry Cohn, 2025.
5 241 0.796065311911 Henry Cohn, 2025.
5 242 0.796930028362 Henry Cohn, 2025.
5 243 0.797123580924 Henry Cohn, 2026, needs more optimization.
5 244 0.797604028749 Henry Cohn, 2026, needs more optimization.
5 245 0.797916847251 Henry Cohn, 2025.
5 246 0.798283603534 Henry Cohn, 2025.
5 247 0.798790606421 Henry Cohn, 2025.
5 248 0.799294089857 Henry Cohn, 2025.
5 249 0.799665163470 Henry Cohn, 2025.
5 250 0.799687724511 Henry Cohn, 2026, needs more optimization.
5 251 0.799695494157 Henry Cohn, 2026, needs more optimization.
5 252 0.800042141214 Henry Cohn, 2026, needs more optimization.
5 253 0.800361794284 Henry Cohn, 2026, needs more optimization.
5 254 0.800542384474 Henry Cohn, 2026, needs more optimization.
5 255 0.801468669593 Henry Cohn, 2026, needs more optimization.
5 256 0.801475125011 Henry Cohn, 2026, needs more optimization.
5 257 0.802206877452 Henry Cohn, 2026, needs more optimization.
5 258 0.802656826349 Henry Cohn, 2025, needs more optimization.
5 259 0.802675225550 Henry Cohn, 2025, needs more optimization.
5 260 0.802955606789 Henry Cohn, 2026, needs more optimization.
5 261 0.803531206141 Henry Cohn, 2026, needs more optimization.
5 262 0.803924735750 Henry Cohn, 2026, needs more optimization.
5 263 0.804141588076 Henry Cohn, 2026, needs more optimization.
5 264 0.804511457554 Henry Cohn, 2026, needs more optimization.
5 265 0.804525832482 Henry Cohn, 2026, needs more optimization.
5 266 0.805070511691 Henry Cohn, 2025, needs more optimization.
5 267 0.805182447272 Henry Cohn, 2026, needs more optimization.
5 268 0.805447930744 Henry Cohn, 2026, needs more optimization.
5 269 0.805694705601 Henry Cohn, 2026, needs more optimization.
5 270 0.805892214741 Henry Cohn, 2026, needs more optimization.
5 271 0.806104593335 Henry Cohn, 2026, needs more optimization.
5 272 0.806492034146 Henry Cohn, 2025, needs more optimization.
5 274 0.806559079295 Henry Cohn, 2026, needs more optimization.
5 275 0.806633113314 Henry Cohn, 2026, needs more optimization.
5 276 0.806749803460 Henry Cohn, 2026, needs more optimization.
5 277 0.806878203435 Henry Cohn, 2026, needs more optimization.
5 279 0.807069479288 Henry Cohn, 2026, needs more optimization.
5 280 0.807210314038 Henry Cohn, 2026, needs more optimization.
5 281 0.807260409149 Henry Cohn, 2026, needs more optimization.
5 282 0.807790416393 Henry Cohn, 2026, needs more optimization.
5 283 0.807990452871 Henry Cohn, 2026, needs more optimization.
5 284 0.808502441915 Henry Cohn, 2025, needs more optimization.
5 285 0.809222044082 Henry Cohn, 2025, needs more optimization.
5 286 0.809311967369 Henry Cohn, 2026, needs more optimization.
5 287 0.809859358344 Henry Cohn, 2026, needs more optimization.
5 288 0.810387182281 Henry Cohn, 2026, needs more optimization.
5 289 0.810515942365 Henry Cohn, 2026, needs more optimization.
5 290 0.811849330647 Henry Cohn, 2026, needs more optimization.
5 291 0.812038638659 Henry Cohn, 2025, needs more optimization.
5 292 0.812315403741 Henry Cohn, 2026, needs more optimization.
5 293 0.812784716715 Henry Cohn, 2026, needs more optimization.
5 294 0.813162150808 Henry Cohn, 2026, needs more optimization.
5 295 0.813794458355 Henry Cohn, 2026, needs more optimization.
5 296 0.814121903369 Henry Cohn, 2026, needs more optimization.
5 297 0.815118059518 Henry Cohn, 2026, needs more optimization.
5 298 0.815629330255 Henry Cohn, 2026, needs more optimization.
5 299 0.816118912242 Henry Cohn, 2026, needs more optimization.
5 300 0.816515571492 Henry Cohn, 2025, needs more optimization.
5 301 0.816884029652 Henry Cohn, 2025, needs more optimization.
5 302 0.817416382715 Henry Cohn, 2026, needs more optimization.
5 303 0.817678249405 Henry Cohn, 2025, needs more optimization.
5 304 0.818236802717 Henry Cohn, 2026, needs more optimization.
5 305 0.818530915024 Henry Cohn, 2025, needs more optimization.
5 306 0.818846725648 Henry Cohn, 2026, needs more optimization.
5 307 0.819649993393 Ilmari Vahteristo, 2026.
5 308 0.819704042350 Henry Cohn, 2025, needs more optimization.
5 309 0.820136258550 Henry Cohn, 2025, needs more optimization.
5 310 0.820291870315 Henry Cohn, 2025, needs more optimization.
5 311 0.820683934305 Henry Cohn, 2025, needs more optimization.
5 312 0.820907477416 Henry Cohn, 2025, needs more optimization.
5 313 0.821238678583 Henry Cohn, 2025, needs more optimization.
5 314 0.821842718616 Henry Cohn, 2025, needs more optimization.
5 315 0.822166006099 Henry Cohn, 2025, needs more optimization.
5 316 0.822348273561 Henry Cohn, 2026, needs more optimization.
5 317 0.822600119096 Henry Cohn, 2025, needs more optimization.
5 318 0.822851367310 Henry Cohn, 2025, needs more optimization.
5 319 0.823386083659 Henry Cohn, 2026, needs more optimization.
5 321 0.823945293516 Henry Cohn, 2025, needs more optimization.
5 322 0.824227974650 Henry Cohn, 2026, needs more optimization.
5 323 0.824521620521 Henry Cohn, 2025, needs more optimization.
5 324 0.824672784814 Ilmari Vahteristo, 2026.
5 325 0.825136817529 Henry Cohn, 2026, needs more optimization.
5 326 0.825465801700 Henry Cohn, 2025, needs more optimization.
5 327 0.825636523896 Henry Cohn, 2026, needs more optimization.
5 328 0.826102388552 Henry Cohn, 2025, needs more optimization.
5 329 0.826424481057 Ilmari Vahteristo, 2026.
5 331 0.826573216614 Ilmari Vahteristo, 2026.
5 332 0.827012207972 Ilmari Vahteristo, 2026.
5 333 0.827486994092 Ilmari Vahteristo, 2026.
5 334 0.827773996545 Ilmari Vahteristo, 2026.
5 335 0.828006262238 Henry Cohn, 2026, needs more optimization.
5 336 0.828034033820 Ilmari Vahteristo, 2026.
5 337 0.828501751462 Ilmari Vahteristo, 2026.
5 338 0.828788070280 Henry Cohn, 2026, needs more optimization.
5 339 0.828788082318 Ilmari Vahteristo, 2026.
5 340 0.829152368222 Henry Cohn, 2025, needs more optimization.
5 341 0.829388117676 Henry Cohn, 2026, needs more optimization.
5 342 0.829749117524 Henry Cohn, 2025, needs more optimization.
5 343 0.829988638760 Ilmari Vahteristo, 2026.
5 344 0.830288948112 Henry Cohn, 2025, needs more optimization.
5 345 0.830334873964 Ilmari Vahteristo, 2026.
5 346 0.830743543200 Henry Cohn, 2025, needs more optimization.
5 347 0.830944830997 Ilmari Vahteristo, 2026.
5 348 0.831093213465 Ilmari Vahteristo, 2026.
5 349 0.831549947592 Henry Cohn, 2026, needs more optimization.
5 350 0.831603555680 Henry Cohn, 2026, needs more optimization.
5 351 0.831919598187 Henry Cohn, 2025, needs more optimization.
5 352 0.831978050097 Ilmari Vahteristo, 2026.
5 353 0.832359675560 Ilmari Vahteristo, 2026.
5 354 0.832781308439 Ilmari Vahteristo, 2026.
5 355 0.832820133321 Ilmari Vahteristo, 2026.
5 356 0.833098647880 Ilmari Vahteristo, 2026.
5 357 0.833368449930 Henry Cohn, 2025, needs more optimization.
5 358 0.833452870525 Henry Cohn, 2025, needs more optimization.
5 359 0.833777259172 Ilmari Vahteristo, 2026.
5 360 0.833869567239 Henry Cohn, 2026, needs more optimization.
5 361 0.834182975616 Henry Cohn, 2025, needs more optimization.
5 362 0.834274529233 Henry Cohn, 2026, needs more optimization.
5 363 0.834618950083 Henry Cohn, 2025, needs more optimization.
5 364 0.834837068276 Henry Cohn, 2026, needs more optimization.
5 365 0.835048430244 Henry Cohn, 2026, needs more optimization.
5 366 0.835387548410 Henry Cohn, 2025, needs more optimization.
5 367 0.835389435183 Henry Cohn, 2025, needs more optimization.
5 368 0.835712494152 Henry Cohn, 2026, needs more optimization.
5 369 0.835765894972 Henry Cohn, 2025, needs more optimization.
5 370 0.836140292070 Henry Cohn, 2026, needs more optimization.
5 371 0.836473545501 Henry Cohn, 2025, needs more optimization.
5 372 0.836679323230 Henry Cohn, 2026, needs more optimization.
5 373 0.836702413007 Henry Cohn, 2026, needs more optimization.
5 374 0.836999067577 Henry Cohn, 2026, needs more optimization.
5 375 0.837271070757 Henry Cohn, 2025, needs more optimization.
5 376 0.837539201868 Henry Cohn, 2025, needs more optimization.
5 377 0.837708951550 Henry Cohn, 2025, needs more optimization.
5 378 0.838003296452 Henry Cohn, 2025, needs more optimization.
5 379 0.838083866651 Henry Cohn, 2026, needs more optimization.
5 380 0.838327924680 Henry Cohn, 2025, needs more optimization.
5 381 0.838354217251 Henry Cohn, 2025, needs more optimization.
5 382 0.838798152226 Henry Cohn, 2025, needs more optimization.
5 383 0.838881488627 Henry Cohn, 2025, needs more optimization.
5 384 0.839339620040 Henry Cohn, 2025, needs more optimization.
5 385 0.839355829121 Henry Cohn, 2025, needs more optimization.
5 386 0.839622713054 Henry Cohn, 2026, needs more optimization.
5 387 0.839804191321 Henry Cohn, 2026, needs more optimization.
5 388 0.839991024596 Henry Cohn, 2025, needs more optimization.
5 389 0.840516182174 Henry Cohn, 2026, needs more optimization.
5 390 0.840803815311 Henry Cohn, 2025, needs more optimization.
5 391 0.840904105112 Henry Cohn, 2026, needs more optimization.
5 392 0.840920101150 Henry Cohn, 2026, needs more optimization.
5 393 0.841234032091 Henry Cohn, 2025, needs more optimization.
5 394 0.841517571002 Henry Cohn, 2025, needs more optimization.
5 395 0.841518430864 Henry Cohn, 2025, needs more optimization.
5 396 0.841721666351 Henry Cohn, 2026, needs more optimization.
5 397 0.841929833352 Henry Cohn, 2026, needs more optimization.
5 398 0.842019642437 Henry Cohn, 2025, needs more optimization.
5 399 0.842351224361 Henry Cohn, 2025, needs more optimization.
5 400 0.842667381746 Henry Cohn, 2026, needs more optimization.
5 401 0.842755099804 Henry Cohn, 2025, needs more optimization.
5 402 0.843048678997 Henry Cohn, 2026, needs more optimization.
5 403 0.843178483011 Henry Cohn, 2025, needs more optimization.
5 404 0.843229111918 Henry Cohn, 2026, needs more optimization.
5 405 0.843596031205 Henry Cohn, 2025, needs more optimization.
5 406 0.843634615469 Henry Cohn, 2025, needs more optimization.
5 407 0.843834979070 Henry Cohn, 2025, needs more optimization.
5 408 0.843903654365 Henry Cohn, 2026, needs more optimization.
5 409 0.843990630575 Henry Cohn, 2025, needs more optimization.
5 410 0.844138429797 Henry Cohn, 2025, needs more optimization.
5 411 0.844505725469 Henry Cohn, 2026, needs more optimization.
5 412 0.844673191519 Henry Cohn, 2026, needs more optimization.
5 413 0.844824973155 Henry Cohn, 2025, needs more optimization.
5 414 0.844870169871 Henry Cohn, 2025, needs more optimization.
5 415 0.845396059797 Henry Cohn, 2025, needs more optimization.
5 416 0.845502920468 Henry Cohn, 2025, needs more optimization.
5 417 0.845632826733 Henry Cohn, 2025, needs more optimization.
5 418 0.845740891849 Henry Cohn, 2026, needs more optimization.
5 419 0.845818752271 Henry Cohn, 2025, needs more optimization.
5 420 0.845998590783 Henry Cohn, 2026, needs more optimization.
5 421 0.846210387692 Henry Cohn, 2026, needs more optimization.
5 422 0.846488117361 Henry Cohn, 2025, needs more optimization.
5 423 0.846740415916 Henry Cohn, 2025, needs more optimization.
5 424 0.846828782623 Henry Cohn, 2026, needs more optimization.
5 425 0.847111917510 Henry Cohn, 2026, needs more optimization.
5 426 0.847141264817 Henry Cohn, 2025, needs more optimization.
5 427 0.847356510265 Henry Cohn, 2026, needs more optimization.
5 428 0.847780543164 Henry Cohn, 2026, needs more optimization.
5 429 0.847871831387 Henry Cohn, 2026, needs more optimization.
5 430 0.848148846253 Henry Cohn, 2025, needs more optimization.
5 431 0.848182648352 Henry Cohn, 2026, needs more optimization.
5 432 0.848428081817 Henry Cohn, 2025, needs more optimization.
5 433 0.848473227014 Henry Cohn, 2025, needs more optimization.
5 434 0.848750844911 Henry Cohn, 2026, needs more optimization.
5 435 0.848935967498 Henry Cohn, 2025, needs more optimization.
5 436 0.849091145842 Henry Cohn, 2026, needs more optimization.
5 437 0.849166823783 Henry Cohn, 2025, needs more optimization.
5 438 0.849457353237 Henry Cohn, 2026, needs more optimization.
5 439 0.849665555849 Henry Cohn, 2026, needs more optimization.
5 440 0.849761491108 Henry Cohn, 2026, needs more optimization.
5 441 0.849905344307 Henry Cohn, 2026, needs more optimization.
5 442 0.850005854540 Henry Cohn, 2026, needs more optimization.
5 443 0.850173997001 Henry Cohn, 2026, needs more optimization.
5 444 0.850591420205 Henry Cohn, 2025, needs more optimization.
5 445 0.850688858705 Henry Cohn, 2025, needs more optimization.
5 446 0.850872757151 Henry Cohn, 2026, needs more optimization.
5 447 0.851046882825 Henry Cohn, 2025, needs more optimization.
5 448 0.851136609114 Henry Cohn, 2026, needs more optimization.
5 449 0.851144183240 Henry Cohn, 2025, needs more optimization.
5 450 0.851519869513 Henry Cohn, 2025, needs more optimization.
5 451 0.851797504621 Henry Cohn, 2025, needs more optimization.
5 452 0.851801424273 Henry Cohn, 2026, needs more optimization.
5 453 0.852169963403 Henry Cohn, 2026, needs more optimization.
5 454 0.852178960242 Henry Cohn, 2026, needs more optimization.
5 455 0.852341044858 Henry Cohn, 2026, needs more optimization.
5 456 0.852509268186 Henry Cohn, 2026, needs more optimization.
5 457 0.852749067895 Henry Cohn, 2025, needs more optimization.
5 458 0.852757857919 Henry Cohn, 2025, needs more optimization.
5 459 0.852826843904 Henry Cohn, 2026, needs more optimization.
5 460 0.853097261023 Henry Cohn, 2026, needs more optimization.
5 461 0.853282800509 Henry Cohn, 2026, needs more optimization.
5 462 0.853613227584 Henry Cohn, 2026, needs more optimization.
5 463 0.853616344570 Henry Cohn, 2025, needs more optimization.
5 464 0.853696327126 Henry Cohn, 2026, needs more optimization.
5 465 0.853910231679 Henry Cohn, 2025, needs more optimization.
5 466 0.854125175508 Henry Cohn, 2025, needs more optimization.
5 467 0.854126192783 Henry Cohn, 2026, needs more optimization.
5 468 0.854465241932 Henry Cohn, 2025, needs more optimization.
5 469 0.854481278069 Henry Cohn, 2026, needs more optimization.
5 470 0.854683349001 Henry Cohn, 2025, needs more optimization.
5 471 0.854796588645 Henry Cohn, 2026, needs more optimization.
5 472 0.854963819384 Henry Cohn, 2025, needs more optimization.
5 473 0.855271668132 Henry Cohn, 2025, needs more optimization.
5 474 0.855274943930 Henry Cohn, 2025, needs more optimization.
5 475 0.855315364840 Henry Cohn, 2025, needs more optimization.
5 476 0.855484878935 Henry Cohn, 2026, needs more optimization.
5 477 0.855695759041 Henry Cohn, 2025, needs more optimization.
5 478 0.855841719507 Henry Cohn, 2026, needs more optimization.
5 479 0.856359033178 Henry Cohn, 2026, needs more optimization.
5 481 0.856438290668 Henry Cohn, 2025, needs more optimization.
5 482 0.856479136994 Henry Cohn, 2025, needs more optimization.
5 483 0.856712971651 Henry Cohn, 2025, needs more optimization.
5 484 0.856722994352 Henry Cohn, 2025, needs more optimization.
5 485 0.856820007940 Henry Cohn, 2025, needs more optimization.
5 486 0.857094821423 Henry Cohn, 2025, needs more optimization.
5 487 0.857117989588 Henry Cohn, 2025, needs more optimization.
5 488 0.857287179940 Henry Cohn, 2025, needs more optimization.
5 489 0.857435857392 Henry Cohn, 2025, needs more optimization.
5 490 0.857565211369 Henry Cohn, 2025, needs more optimization.
5 491 0.857620435328 Henry Cohn, 2025, needs more optimization.
5 492 0.857846614823 Henry Cohn, 2025, needs more optimization.
5 493 0.857887587311 Henry Cohn, 2026, needs more optimization.
5 494 0.857985545441 Henry Cohn, 2025, needs more optimization.
5 495 0.858367120376 Henry Cohn, 2025, needs more optimization.
5 496 0.858507150778 Henry Cohn, 2025, needs more optimization.
5 497 0.858685307857 Henry Cohn, 2025, needs more optimization.
5 498 0.858833192245 Henry Cohn, 2025, needs more optimization.
5 499 0.858944591166 Henry Cohn, 2026, needs more optimization.
5 500 0.859136977171 Henry Cohn, 2025, needs more optimization.
5 501 0.859512033864 Henry Cohn, 2025, needs more optimization.
5 502 0.859555607488 Henry Cohn, 2026, needs more optimization.
5 503 0.859590934115 Henry Cohn, 2025, needs more optimization.
5 504 0.859701419249 Henry Cohn, 2026, needs more optimization.
5 505 0.859778505009 Henry Cohn, 2025, needs more optimization.
5 506 0.859876844867 Henry Cohn, 2025, needs more optimization.
5 507 0.860054961546 Henry Cohn, 2026, needs more optimization.
5 508 0.860267863182 Henry Cohn, 2026, needs more optimization.
5 509 0.860322505942 Henry Cohn, 2025, needs more optimization.
5 510 0.860628775031 Henry Cohn, 2025, needs more optimization.
5 511 0.860697231201 Henry Cohn, 2025, needs more optimization.
5 512 0.860725260477 Henry Cohn, 2025, needs more optimization.
5 513 0.860797749661 Henry Cohn, 2026, needs more optimization.
5 515 0.861143775119 Henry Cohn, 2026, needs more optimization.
5 516 0.861368957008 Henry Cohn, 2025, needs more optimization.
5 517 0.861388637378 Henry Cohn, 2026, needs more optimization.
5 518 0.861543720608 Henry Cohn, 2025, needs more optimization.
5 519 0.861749444634 Henry Cohn, 2026, needs more optimization.
5 520 0.861749994508 Henry Cohn, 2026, needs more optimization.
5 521 0.861795267361 Henry Cohn, 2025, needs more optimization.
5 522 0.862091307594 Henry Cohn, 2025, needs more optimization.
5 523 0.862318412803 Henry Cohn, 2025, needs more optimization.
5 524 0.862466887973 Henry Cohn, 2026, needs more optimization.
5 525 0.862470664059 Henry Cohn, 2025, needs more optimization.
5 526 0.862683702407 Henry Cohn, 2025, needs more optimization.
5 527 0.862707887103 Henry Cohn, 2026, needs more optimization.
5 528 0.862884014457 Henry Cohn, 2026, needs more optimization.
5 529 0.863035952578 Henry Cohn, 2025, needs more optimization.
5 530 0.863104542022 Henry Cohn, 2026, needs more optimization.
5 531 0.863240337579 Henry Cohn, 2025, needs more optimization.
5 532 0.863458712182 Henry Cohn, 2026, needs more optimization.
5 533 0.863618313032 Henry Cohn, 2026, needs more optimization.
5 534 0.863843381931 Henry Cohn, 2025, needs more optimization.
5 535 0.863880240397 Henry Cohn, 2025, needs more optimization.
5 536 0.863923777463 Henry Cohn, 2025, needs more optimization.
5 537 0.864152691676 Henry Cohn, 2026, needs more optimization.
5 538 0.864154701351 Henry Cohn, 2025, needs more optimization.
5 540 0.864395058631 Henry Cohn, 2025, needs more optimization.
5 542 0.864745296806 Henry Cohn, 2025, needs more optimization.
5 543 0.864969144430 Henry Cohn, 2026, needs more optimization.
5 544 0.864997867521 Henry Cohn, 2025, needs more optimization.
5 545 0.865069847868 Henry Cohn, 2025, needs more optimization.
5 546 0.865281323991 Henry Cohn, 2026, needs more optimization.
5 547 0.865434209594 Henry Cohn, 2026, needs more optimization.
5 548 0.865438315541 Henry Cohn, 2026, needs more optimization.
5 549 0.865712585376 Henry Cohn, 2025, needs more optimization.
5 550 0.865824560652 Henry Cohn, 2026, needs more optimization.
5 551 0.865842695323 Henry Cohn, 2026, needs more optimization.
5 552 0.865879307122 Henry Cohn, 2025, needs more optimization.
5 553 0.866159324412 Henry Cohn, 2025, needs more optimization.
5 554 0.866200338542 Henry Cohn, 2025, needs more optimization.
5 555 0.866352525315 Henry Cohn, 2025, needs more optimization.
5 556 0.866362800622 Henry Cohn, 2025, needs more optimization.
5 557 0.866758622688 Henry Cohn, 2026, needs more optimization.
5 558 0.866872959031 Henry Cohn, 2025, needs more optimization.
5 559 0.866900685443 Henry Cohn, 2025, needs more optimization.
5 560 0.867099425536 Henry Cohn, 2025, needs more optimization.
5 561 0.867325322385 Henry Cohn, 2025, needs more optimization.
5 562 0.867343447361 Henry Cohn, 2025, needs more optimization.
5 563 0.867436150282 Henry Cohn, 2025, needs more optimization.
5 564 0.867447737084 Henry Cohn, 2026, needs more optimization.
5 565 0.867452395939 Henry Cohn, 2025, needs more optimization.
5 566 0.867653917205 Henry Cohn, 2025, needs more optimization.
5 567 0.867784283396 Henry Cohn, 2026, needs more optimization.
5 568 0.867887760645 Henry Cohn, 2025, needs more optimization.
5 569 0.868077290034 Henry Cohn, 2025, needs more optimization.
5 570 0.868216680382 Henry Cohn, 2025, needs more optimization.
5 572 0.868451973652 Henry Cohn, 2026, needs more optimization.
5 573 0.868654373375 Henry Cohn, 2025, needs more optimization.
5 574 0.868673755205 Henry Cohn, 2025, needs more optimization.
5 575 0.868676712166 Henry Cohn, 2026, needs more optimization.
5 577 0.868935335122 Henry Cohn, 2025, needs more optimization.
5 578 0.868981819142 Henry Cohn, 2025, needs more optimization.
5 579 0.869153575403 Henry Cohn, 2026, needs more optimization.
5 580 0.869345631288 Henry Cohn, 2025, needs more optimization.
5 581 0.869468305984 Henry Cohn, 2025, needs more optimization.
5 582 0.869569569795 Henry Cohn, 2025, needs more optimization.
5 583 0.869749722833 Henry Cohn, 2026, needs more optimization.
5 584 0.869920874945 Henry Cohn, 2026, needs more optimization.
5 585 0.869929165808 Henry Cohn, 2026, needs more optimization.
5 586 0.870175585547 Henry Cohn, 2025, needs more optimization.
5 587 0.870179294621 Henry Cohn, 2025, needs more optimization.
5 588 0.870186408492 Henry Cohn, 2026, needs more optimization.
5 589 0.870249803628 Henry Cohn, 2025, needs more optimization.
5 590 0.870385377115 Henry Cohn, 2025, needs more optimization.
5 591 0.870414929971 Henry Cohn, 2025, needs more optimization.
5 592 0.870655172327 Henry Cohn, 2026, needs more optimization.
5 593 0.870691681545 Henry Cohn, 2026, needs more optimization.
5 594 0.870810238973 Henry Cohn, 2026, needs more optimization.
5 595 0.871066955540 Henry Cohn, 2025, needs more optimization.
5 596 0.871070914052 Henry Cohn, 2026, needs more optimization.
5 597 0.871105033160 Henry Cohn, 2025, needs more optimization.
5 598 0.871326407700 Henry Cohn, 2025, needs more optimization.
5 599 0.871327354638 Henry Cohn, 2026, needs more optimization.
5 600 0.871382362457 Henry Cohn, 2026, needs more optimization.
5 601 0.871604091828 Henry Cohn, 2026, needs more optimization.
5 602 0.871606438312 Henry Cohn, 2025, needs more optimization.
5 603 0.871665796035 Henry Cohn, 2026, needs more optimization.
5 604 0.871805838747 Henry Cohn, 2026, needs more optimization.
5 605 0.871824322660 Henry Cohn, 2025, needs more optimization.
5 606 0.871902403634 Henry Cohn, 2026, needs more optimization.
5 607 0.872081555797 Henry Cohn, 2026, needs more optimization.
5 608 0.872084141228 Henry Cohn, 2026, needs more optimization.
5 609 0.872517588599 Henry Cohn, 2026, needs more optimization.
5 610 0.872521651154 Henry Cohn, 2026, needs more optimization.
5 611 0.872670113057 Henry Cohn, 2025, needs more optimization.
5 612 0.872701370708 Henry Cohn, 2026, needs more optimization.
5 613 0.872895228619 Henry Cohn, 2026, needs more optimization.
5 614 0.872896331494 Henry Cohn, 2026, needs more optimization.
5 615 0.873090713168 Henry Cohn, 2025, needs more optimization.
5 616 0.873103833019 Henry Cohn, 2026, needs more optimization.
5 617 0.873301059105 Henry Cohn, 2025, needs more optimization.
5 618 0.873380978365 Henry Cohn, 2025, needs more optimization.
5 619 0.873472760121 Henry Cohn, 2026, needs more optimization.
5 620 0.873605610177 Henry Cohn, 2026, needs more optimization.
5 621 0.873622039759 Henry Cohn, 2025, needs more optimization.
5 622 0.873753446890 Henry Cohn, 2025, needs more optimization.
5 623 0.873905770256 Henry Cohn, 2025, needs more optimization.
5 624 0.873949410115 Henry Cohn, 2026, needs more optimization.
5 625 0.874124521820 Henry Cohn, 2026, needs more optimization.
5 626 0.874138805817 Henry Cohn, 2025, needs more optimization.
5 627 0.874162709567 Henry Cohn, 2025, needs more optimization.
5 628 0.874359782501 Henry Cohn, 2026, needs more optimization.
5 629 0.874485297919 Henry Cohn, 2025, needs more optimization.
5 630 0.874703509407 Henry Cohn, 2025, needs more optimization.
5 631 0.874836646897 Henry Cohn, 2026, needs more optimization.
5 633 0.874969572156 Henry Cohn, 2025, needs more optimization.
5 634 0.874987432232 Henry Cohn, 2026, needs more optimization.
5 635 0.875121083724 Henry Cohn, 2026, needs more optimization.
5 636 0.875300468091 Henry Cohn, 2025, needs more optimization.
5 637 0.875307252400 Henry Cohn, 2025, needs more optimization.
5 638 0.875387823448 Henry Cohn, 2025, needs more optimization.
5 639 0.875463236969 Henry Cohn, 2025, needs more optimization.
5 640 0.875640540653 Henry Cohn, 2026, needs more optimization.
5 641 0.875645428560 Henry Cohn, 2026, needs more optimization.
5 642 0.875664298640 Henry Cohn, 2025, needs more optimization.
5 643 0.875835676045 Henry Cohn, 2025, needs more optimization.
5 644 0.876028785170 Henry Cohn, 2026, needs more optimization.
5 645 0.876115945893 Henry Cohn, 2026, needs more optimization.
5 646 0.876190173583 Henry Cohn, 2026, needs more optimization.
5 647 0.876317790109 Henry Cohn, 2026, needs more optimization.
5 648 0.876321229584 Henry Cohn, 2025, needs more optimization.
5 649 0.876512730152 Henry Cohn, 2026, needs more optimization.
5 650 0.876534189853 Henry Cohn, 2025, needs more optimization.
5 651 0.876643344064 Henry Cohn, 2026, needs more optimization.
5 652 0.876649196799 Henry Cohn, 2025, needs more optimization.
5 653 0.876891012640 Henry Cohn, 2025, needs more optimization.
5 654 0.877000319265 Henry Cohn, 2025, needs more optimization.
5 655 0.877194944627 Henry Cohn, 2025, needs more optimization.
5 656 0.877250936425 Henry Cohn, 2026, needs more optimization.
5 657 0.877335064927 Henry Cohn, 2026, needs more optimization.
5 659 0.877422215326 Henry Cohn, 2025, needs more optimization.
5 660 0.877460598524 Henry Cohn, 2026, needs more optimization.
5 661 0.877492961756 Henry Cohn, 2025, needs more optimization.
5 662 0.877622878303 Henry Cohn, 2025, needs more optimization.
5 663 0.877665604940 Henry Cohn, 2025, needs more optimization.
5 664 0.877808986150 Henry Cohn, 2025, needs more optimization.
5 665 0.877818204583 Henry Cohn, 2025, needs more optimization.
5 666 0.877882963051 Henry Cohn, 2025, needs more optimization.
5 667 0.878015154801 Henry Cohn, 2025, needs more optimization.
5 668 0.878121319924 Henry Cohn, 2026, needs more optimization.
5 669 0.878257366556 Henry Cohn, 2026, needs more optimization.
5 670 0.878394096821 Henry Cohn, 2025, needs more optimization.
5 671 0.878396868361 Henry Cohn, 2026, needs more optimization.
5 672 0.878555950413 Henry Cohn, 2026, needs more optimization.
5 673 0.878568357345 Henry Cohn, 2025, needs more optimization.
5 674 0.878677355021 Henry Cohn, 2025, needs more optimization.
5 675 0.878691240621 Henry Cohn, 2026, needs more optimization.
5 676 0.878895335529 Henry Cohn, 2025, needs more optimization.
5 677 0.879051400128 Henry Cohn, 2026, needs more optimization.
5 678 0.879056198237 Henry Cohn, 2025, needs more optimization.
5 680 0.879254843264 Henry Cohn, 2025, needs more optimization.
5 681 0.879266797921 Henry Cohn, 2025, needs more optimization.
5 683 0.879420942902 Henry Cohn, 2026, needs more optimization.
5 685 0.879604768234 Henry Cohn, 2025, needs more optimization.
5 686 0.879615298504 Henry Cohn, 2025, needs more optimization.
5 687 0.879927224792 Henry Cohn, 2025, needs more optimization.
5 688 0.879940879306 Henry Cohn, 2025, needs more optimization.
5 689 0.880050272700 Henry Cohn, 2025, needs more optimization.
5 690 0.880076920142 Henry Cohn, 2026, needs more optimization.
5 691 0.880186913631 Henry Cohn, 2025, needs more optimization.
5 692 0.880342004990 Henry Cohn, 2026, needs more optimization.
5 693 0.880342482614 Henry Cohn, 2026, needs more optimization.
5 694 0.880434990743 Henry Cohn, 2026, needs more optimization.
5 695 0.880560210580 Henry Cohn, 2025, needs more optimization.
5 696 0.880565807461 Henry Cohn, 2026, needs more optimization.
5 697 0.880726173156 Henry Cohn, 2026, needs more optimization.
5 698 0.880748341053 Henry Cohn, 2026, needs more optimization.
5 699 0.880831552541 Henry Cohn, 2025, needs more optimization.
5 700 0.880840937215 Henry Cohn, 2026, needs more optimization.
5 701 0.881073608246 Henry Cohn, 2026, needs more optimization.
5 702 0.881075411709 Henry Cohn, 2026, needs more optimization.
5 703 0.881076952719 Henry Cohn, 2026, needs more optimization.
5 704 0.881254031900 Henry Cohn, 2026, needs more optimization.
5 705 0.881266162475 Henry Cohn, 2025, needs more optimization.
5 706 0.881503126136 Henry Cohn, 2026, needs more optimization.
5 707 0.881504079243 Henry Cohn, 2026, needs more optimization.
5 708 0.881611839007 Henry Cohn, 2026, needs more optimization.
5 709 0.881738346869 Henry Cohn, 2026, needs more optimization.
5 710 0.881746195595 Henry Cohn, 2025, needs more optimization.
5 711 0.881850335459 Henry Cohn, 2025, needs more optimization.
5 712 0.881972602373 Henry Cohn, 2026, needs more optimization.
5 713 0.882012668941 Henry Cohn, 2025, needs more optimization.
5 714 0.882161638275 Henry Cohn, 2025, needs more optimization.
5 715 0.882184668744 Henry Cohn, 2026, needs more optimization.
5 716 0.882320732625 Henry Cohn, 2025, needs more optimization.
5 717 0.882323465849 Henry Cohn, 2026, needs more optimization.
5 718 0.882448099525 Henry Cohn, 2026, needs more optimization.
5 719 0.882451993509 Henry Cohn, 2026, needs more optimization.
5 720 0.882579799033 Henry Cohn, 2026, needs more optimization.
5 721 0.882850229503 Henry Cohn, 2025, needs more optimization.
5 722 0.882852390341 Henry Cohn, 2026, needs more optimization.
5 723 0.882955687290 Henry Cohn, 2025, needs more optimization.
5 724 0.882977268110 Henry Cohn, 2026, needs more optimization.
5 725 0.882978206211 Henry Cohn, 2026, needs more optimization.
5 726 0.883106952536 Henry Cohn, 2025, needs more optimization.
5 727 0.883131612758 Henry Cohn, 2025, needs more optimization.
5 728 0.883292687410 Henry Cohn, 2026, needs more optimization.
5 729 0.883327308778 Henry Cohn, 2025, needs more optimization.
5 730 0.883442618904 Henry Cohn, 2026, needs more optimization.
5 731 0.883524469603 Henry Cohn, 2026, needs more optimization.
5 732 0.883524699608 Henry Cohn, 2025, needs more optimization.
5 733 0.883673967839 Henry Cohn, 2025, needs more optimization.
5 734 0.883710902643 Henry Cohn, 2026, needs more optimization.
5 735 0.883861020714 Henry Cohn, 2026, needs more optimization.
5 736 0.883894566369 Henry Cohn, 2026, needs more optimization.
5 737 0.883899759689 Henry Cohn, 2025, needs more optimization.
5 738 0.883986347823 Henry Cohn, 2025, needs more optimization.
5 739 0.884167589206 Henry Cohn, 2025, needs more optimization.
5 740 0.884196725787 Henry Cohn, 2026, needs more optimization.
5 741 0.884317424162 Henry Cohn, 2026, needs more optimization.
5 742 0.884402016745 Henry Cohn, 2026, needs more optimization.
5 743 0.884526608919 Henry Cohn, 2025, needs more optimization.
5 744 0.884643952628 Henry Cohn, 2026, needs more optimization.
5 745 0.884681580162 Henry Cohn, 2026, needs more optimization.
5 746 0.884791620398 Henry Cohn, 2026, needs more optimization.
5 747 0.884903075377 Henry Cohn, 2025, needs more optimization.
5 748 0.885005159387 Henry Cohn, 2025, needs more optimization.
5 749 0.885008274623 Henry Cohn, 2026, needs more optimization.
5 750 0.885064693816 Henry Cohn, 2026, needs more optimization.
5 751 0.885133168731 Henry Cohn, 2025, needs more optimization.
5 752 0.885244724931 Henry Cohn, 2025, needs more optimization.
5 753 0.885246223059 Henry Cohn, 2026, needs more optimization.
5 754 0.885355810051 Henry Cohn, 2025, needs more optimization.
5 755 0.885389819977 Henry Cohn, 2025, needs more optimization.
5 756 0.885486686725 Henry Cohn, 2026, needs more optimization.
5 757 0.885576627751 Henry Cohn, 2025, needs more optimization.
5 758 0.885608708664 Henry Cohn, 2026, needs more optimization.
5 759 0.885788496516 Henry Cohn, 2025, needs more optimization.
5 760 0.885791735831 Henry Cohn, 2025, needs more optimization.
5 761 0.885915712593 Henry Cohn, 2025, needs more optimization.
5 762 0.885947010386 Henry Cohn, 2026, needs more optimization.
5 763 0.886054211065 Henry Cohn, 2026, needs more optimization.
5 764 0.886068745964 Henry Cohn, 2026, needs more optimization.
5 765 0.886195389172 Henry Cohn, 2025, needs more optimization.
5 766 0.886239507362 Henry Cohn, 2025, needs more optimization.
5 767 0.886286097191 Henry Cohn, 2025, needs more optimization.
5 768 0.886313548380 Henry Cohn, 2026, needs more optimization.
5 769 0.886333828851 Henry Cohn, 2025, needs more optimization.
5 771 0.886566932341 Henry Cohn, 2025, needs more optimization.
5 772 0.886580171023 Henry Cohn, 2026, needs more optimization.
5 773 0.886811509004 Henry Cohn, 2025, needs more optimization.
5 774 0.886818199717 Henry Cohn, 2026, needs more optimization.
5 775 0.886857339438 Henry Cohn, 2025, needs more optimization.
5 776 0.886976946131 Henry Cohn, 2026, needs more optimization.
5 777 0.886986115500 Henry Cohn, 2025, needs more optimization.
5 778 0.887166152141 Henry Cohn, 2025, needs more optimization.
5 779 0.887173485788 Henry Cohn, 2025, needs more optimization.
5 780 0.887282002983 Henry Cohn, 2026, needs more optimization.
5 781 0.887293711372 Henry Cohn, 2026, needs more optimization.
5 782 0.887318221044 Henry Cohn, 2026, needs more optimization.
5 783 0.887387168253 Henry Cohn, 2026, needs more optimization.
5 784 0.887486537415 Henry Cohn, 2026, needs more optimization.
5 785 0.887487426156 Henry Cohn, 2025, needs more optimization.
5 786 0.887548227422 Henry Cohn, 2025, needs more optimization.
5 787 0.887727286658 Henry Cohn, 2025, needs more optimization.
5 788 0.887728284656 Henry Cohn, 2026, needs more optimization.
5 789 0.887822163350 Henry Cohn, 2026, needs more optimization.
5 790 0.887929616199 Henry Cohn, 2025, needs more optimization.
5 791 0.887936822195 Henry Cohn, 2025, needs more optimization.
5 792 0.888004025348 Henry Cohn, 2026, needs more optimization.
5 793 0.888116581586 Henry Cohn, 2025, needs more optimization.
5 794 0.888134980619 Henry Cohn, 2026, needs more optimization.
5 795 0.888214561367 Henry Cohn, 2026, needs more optimization.
5 796 0.888241437301 Henry Cohn, 2026, needs more optimization.
5 797 0.888445319206 Henry Cohn, 2025, needs more optimization.
5 798 0.888463671895 Henry Cohn, 2026, needs more optimization.
5 799 0.888486462856 Henry Cohn, 2025, needs more optimization.
5 800 0.888530875178 Henry Cohn, 2026, needs more optimization.
5 801 0.888651958404 Henry Cohn, 2025, needs more optimization.
5 802 0.888655481864 Henry Cohn, 2025, needs more optimization.
5 803 0.888896550093 Henry Cohn, 2025, needs more optimization.
5 804 0.888903636362 Henry Cohn, 2026, needs more optimization.
5 805 0.888947331540 Henry Cohn, 2026, needs more optimization.
5 806 0.888961995804 Henry Cohn, 2025, needs more optimization.
5 807 0.889157983995 Henry Cohn, 2025, needs more optimization.
5 808 0.889232054009 Henry Cohn, 2026, needs more optimization.
5 809 0.889293843886 Henry Cohn, 2025, needs more optimization.
5 810 0.889368730713 Henry Cohn, 2026, needs more optimization.
5 811 0.889450629631 Henry Cohn, 2026, needs more optimization.
5 812 0.889465251480 Henry Cohn, 2026, needs more optimization.
5 813 0.889601237234 Henry Cohn, 2025, needs more optimization.
5 814 0.889708667362 Henry Cohn, 2025, needs more optimization.
5 815 0.889709777622 Henry Cohn, 2026, needs more optimization.
5 816 0.889735671604 Henry Cohn, 2026, needs more optimization.
5 817 0.889771290214 Henry Cohn, 2025, needs more optimization.
5 818 0.889876459009 Henry Cohn, 2026, needs more optimization.
5 819 0.889885890089 Henry Cohn, 2025, needs more optimization.
5 820 0.889896735801 Henry Cohn, 2026, needs more optimization.
5 822 0.890124860445 Henry Cohn, 2026, needs more optimization.
5 823 0.890285307138 Henry Cohn, 2025, needs more optimization.
5 824 0.890287123138 Henry Cohn, 2026, needs more optimization.
5 825 0.890421726452 Henry Cohn, 2026, needs more optimization.
5 826 0.890422086940 Henry Cohn, 2026, needs more optimization.
5 827 0.890443189481 Henry Cohn, 2025, needs more optimization.
5 828 0.890565574880 Henry Cohn, 2026, needs more optimization.
5 829 0.890617714667 Henry Cohn, 2025, needs more optimization.
5 830 0.890713303532 Henry Cohn, 2026, needs more optimization.
5 831 0.890729720533 Henry Cohn, 2026, needs more optimization.
5 832 0.890754211876 Henry Cohn, 2026, needs more optimization.
5 833 0.890775695838 Henry Cohn, 2025, needs more optimization.
5 834 0.890799815802 Henry Cohn, 2026, needs more optimization.
5 836 0.891033531559 Henry Cohn, 2026, needs more optimization.
5 837 0.891260899176 Henry Cohn, 2025, needs more optimization.
5 838 0.891262029631 Henry Cohn, 2026, needs more optimization.
5 839 0.891295870406 Henry Cohn, 2025, needs more optimization.
5 840 0.891307991324 Henry Cohn, 2026, needs more optimization.
5 841 0.891426470359 Henry Cohn, 2025, needs more optimization.
5 842 0.891451579999 Henry Cohn, 2026, needs more optimization.
5 843 0.891563208434 Henry Cohn, 2025, needs more optimization.
5 844 0.891565320583 Henry Cohn, 2026, needs more optimization.
5 845 0.891706512207 Henry Cohn, 2025, needs more optimization.
5 846 0.891719866224 Henry Cohn, 2026, needs more optimization.
5 847 0.891744709015 Henry Cohn, 2025, needs more optimization.
5 848 0.891879939732 Henry Cohn, 2026, needs more optimization.
5 849 0.891893926884 Henry Cohn, 2025, needs more optimization.
5 850 0.891961059961 Henry Cohn, 2026, needs more optimization.
5 851 0.891972040917 Henry Cohn, 2025, needs more optimization.
5 852 0.892114758060 Henry Cohn, 2025, needs more optimization.
5 853 0.892116266712 Henry Cohn, 2025, needs more optimization.
5 854 0.892203056941 Henry Cohn, 2026, needs more optimization.
5 855 0.892312453139 Henry Cohn, 2025, needs more optimization.
5 856 0.892364658170 Henry Cohn, 2026, needs more optimization.
5 857 0.892374108700 Henry Cohn, 2025, needs more optimization.
5 858 0.892427569330 Henry Cohn, 2026, needs more optimization.
5 860 0.892629264993 Henry Cohn, 2026, needs more optimization.
5 861 0.892631606669 Henry Cohn, 2026, needs more optimization.
5 862 0.892636630150 Henry Cohn, 2025, needs more optimization.
5 863 0.892802953508 Henry Cohn, 2025, needs more optimization.
5 864 0.892813781513 Henry Cohn, 2026, needs more optimization.
5 865 0.892904803395 Henry Cohn, 2026, needs more optimization.
5 866 0.892931703932 Henry Cohn, 2026, needs more optimization.
5 867 0.893069164751 Henry Cohn, 2025, needs more optimization.
5 869 0.893092115983 Henry Cohn, 2025, needs more optimization.
5 870 0.893249121722 Henry Cohn, 2026, needs more optimization.
5 871 0.893285775424 Henry Cohn, 2025, needs more optimization.
5 872 0.893349843187 Henry Cohn, 2026, needs more optimization.
5 873 0.893401125154 Henry Cohn, 2025, needs more optimization.
5 874 0.893405519716 Henry Cohn, 2026, needs more optimization.
5 875 0.893537264211 Henry Cohn, 2026, needs more optimization.
5 876 0.893548204171 Henry Cohn, 2026, needs more optimization.
5 877 0.893675348805 Henry Cohn, 2025, needs more optimization.
5 878 0.893675401364 Henry Cohn, 2026, needs more optimization.
5 879 0.893830168591 Henry Cohn, 2025, needs more optimization.
5 880 0.893831729413 Henry Cohn, 2025, needs more optimization.
5 881 0.893865663145 Henry Cohn, 2025, needs more optimization.
5 882 0.893870916377 Henry Cohn, 2026, needs more optimization.
5 883 0.893951538397 Henry Cohn, 2025, needs more optimization.
5 884 0.894089862035 Henry Cohn, 2025, needs more optimization.
5 885 0.894104455283 Henry Cohn, 2025, needs more optimization.
5 886 0.894271519384 Henry Cohn, 2026, needs more optimization.
5 887 0.894276380550 Henry Cohn, 2026, needs more optimization.
5 888 0.894376187680 Henry Cohn, 2026, needs more optimization.
5 889 0.894397153171 Henry Cohn, 2025, needs more optimization.
5 890 0.894515998427 Henry Cohn, 2026, needs more optimization.
5 891 0.894532550295 Henry Cohn, 2025, needs more optimization.
5 892 0.894550995136 Henry Cohn, 2026, needs more optimization.
5 893 0.894620493080 Henry Cohn, 2025, needs more optimization.
5 894 0.894665448614 Henry Cohn, 2026, needs more optimization.
5 895 0.894667517151 Henry Cohn, 2025, needs more optimization.
5 896 0.894750896742 Henry Cohn, 2025, needs more optimization.
5 897 0.894838699596 Henry Cohn, 2025, needs more optimization.
5 898 0.894839527562 Henry Cohn, 2025, needs more optimization.
5 899 0.894961728514 Henry Cohn, 2025, needs more optimization.
5 900 0.894963952553 Henry Cohn, 2026, needs more optimization.
5 901 0.895053970280 Henry Cohn, 2026, needs more optimization.
5 902 0.895056901178 Henry Cohn, 2025, needs more optimization.
5 903 0.895266108241 Henry Cohn, 2025, needs more optimization.
5 904 0.895275689100 Henry Cohn, 2025, needs more optimization.
5 905 0.895302564593 Henry Cohn, 2025, needs more optimization.
5 906 0.895398566320 Henry Cohn, 2025, needs more optimization.
5 907 0.895399183332 Henry Cohn, 2025, needs more optimization.
5 908 0.895486681607 Henry Cohn, 2026, needs more optimization.
5 909 0.895529684165 Henry Cohn, 2025, needs more optimization.
5 910 0.895634459369 Henry Cohn, 2026, needs more optimization.
5 912 0.895721235146 Henry Cohn, 2026, needs more optimization.
5 913 0.895831413756 Henry Cohn, 2026, needs more optimization.
5 914 0.895864388648 Henry Cohn, 2026, needs more optimization.
5 915 0.895867784677 Henry Cohn, 2026, needs more optimization.
5 916 0.896008207188 Henry Cohn, 2026, needs more optimization.
5 917 0.896010138422 Henry Cohn, 2026, needs more optimization.
5 918 0.896128589466 Henry Cohn, 2026, needs more optimization.
5 919 0.896157599104 Henry Cohn, 2025, needs more optimization.
5 920 0.896279397003 Henry Cohn, 2026, needs more optimization.
5 921 0.896298563295 Henry Cohn, 2025, needs more optimization.
5 922 0.896299418572 Henry Cohn, 2026, needs more optimization.
5 923 0.896387283905 Henry Cohn, 2026, needs more optimization.
5 924 0.896388483329 Henry Cohn, 2026, needs more optimization.
5 925 0.896427119985 Henry Cohn, 2026, needs more optimization.
5 926 0.896481322352 Henry Cohn, 2026, needs more optimization.
5 927 0.896566089205 Henry Cohn, 2026, needs more optimization.
5 928 0.896570399324 Henry Cohn, 2026, needs more optimization.
5 929 0.896664763022 Henry Cohn, 2025, needs more optimization.
5 931 0.896785863752 Henry Cohn, 2026, needs more optimization.
5 932 0.896898653164 Henry Cohn, 2026, needs more optimization.
5 933 0.896903780677 Henry Cohn, 2025, needs more optimization.
5 934 0.897005323952 Henry Cohn, 2026, needs more optimization.
5 935 0.897007731039 Henry Cohn, 2025, needs more optimization.
5 936 0.897038468539 Henry Cohn, 2026, needs more optimization.
5 937 0.897157934409 Henry Cohn, 2025, needs more optimization.
5 938 0.897159993258 Henry Cohn, 2025, needs more optimization.
5 939 0.897264928383 Henry Cohn, 2025, needs more optimization.
5 940 0.897301498985 Henry Cohn, 2026, needs more optimization.
5 941 0.897424645659 Henry Cohn, 2026, needs more optimization.
5 942 0.897428392170 Henry Cohn, 2026, needs more optimization.
5 943 0.897435822418 Henry Cohn, 2025, needs more optimization.
5 944 0.897512142346 Henry Cohn, 2026, needs more optimization.
5 945 0.897673470977 Henry Cohn, 2026, needs more optimization.
5 946 0.897711366435 Henry Cohn, 2026, needs more optimization.
5 947 0.897801351017 Henry Cohn, 2026, needs more optimization.
5 948 0.897802739305 Henry Cohn, 2026, needs more optimization.
5 949 0.897828002885 Henry Cohn, 2025, needs more optimization.
5 950 0.897931543882 Henry Cohn, 2026, needs more optimization.
5 952 0.897962728304 Henry Cohn, 2026, needs more optimization.
5 953 0.898026166430 Henry Cohn, 2026, needs more optimization.
5 954 0.898039568578 Henry Cohn, 2026, needs more optimization.
5 955 0.898064550461 Henry Cohn, 2025, needs more optimization.
5 956 0.898075128638 Henry Cohn, 2025, needs more optimization.
5 957 0.898241407327 Henry Cohn, 2025, needs more optimization.
5 958 0.898247608210 Henry Cohn, 2026, needs more optimization.
5 959 0.898260631410 Henry Cohn, 2025, needs more optimization.
5 960 0.898312398441 Henry Cohn, 2026, needs more optimization.
5 961 0.898393471322 Henry Cohn, 2026, needs more optimization.
5 962 0.898408422618 Henry Cohn, 2026, needs more optimization.
5 963 0.898422521081 Henry Cohn, 2025, needs more optimization.
5 964 0.898521213325 Henry Cohn, 2026, needs more optimization.
5 965 0.898534843820 Henry Cohn, 2025, needs more optimization.
5 966 0.898735260894 Henry Cohn, 2026, needs more optimization.
5 967 0.898736744826 Henry Cohn, 2025, needs more optimization.
5 968 0.898831647675 Henry Cohn, 2026, needs more optimization.
5 969 0.898834405539 Henry Cohn, 2025, needs more optimization.
5 970 0.898855023817 Henry Cohn, 2026, needs more optimization.
5 971 0.898934578212 Henry Cohn, 2026, needs more optimization.
5 972 0.898939223336 Henry Cohn, 2025, needs more optimization.
5 973 0.899008765823 Henry Cohn, 2026, needs more optimization.
5 974 0.899113176274 Henry Cohn, 2026, needs more optimization.
5 975 0.899121313598 Henry Cohn, 2025, needs more optimization.
5 976 0.899130526227 Henry Cohn, 2025, needs more optimization.
5 977 0.899260041990 Henry Cohn, 2025, needs more optimization.
5 978 0.899359638664 Henry Cohn, 2026, needs more optimization.
5 979 0.899371062173 Henry Cohn, 2026, needs more optimization.
5 980 0.899385690646 Henry Cohn, 2026, needs more optimization.
5 981 0.899409604665 Henry Cohn, 2026, needs more optimization.
5 982 0.899488303056 Henry Cohn, 2026, needs more optimization.
5 983 0.899611274544 Henry Cohn, 2026, needs more optimization.
5 984 0.899630531156 Henry Cohn, 2026, needs more optimization.
5 985 0.899632280944 Henry Cohn, 2026, needs more optimization.
5 986 0.899708088763 Henry Cohn, 2025, needs more optimization.
5 987 0.899728049908 Henry Cohn, 2026, needs more optimization.
5 988 0.899890869229 Henry Cohn, 2026, needs more optimization.
5 989 0.899895541128 Henry Cohn, 2025, needs more optimization.
5 990 0.899896298443 Henry Cohn, 2026, needs more optimization.
5 991 0.899929613953 Henry Cohn, 2025, needs more optimization.
5 992 0.899964158387 Henry Cohn, 2026, needs more optimization.
5 993 0.900083161501 Henry Cohn, 2025, needs more optimization.
5 994 0.900135221354 Henry Cohn, 2026, needs more optimization.
5 995 0.900264310026 Henry Cohn, 2025, needs more optimization.
5 996 0.900271407903 Henry Cohn, 2026, needs more optimization.
5 997 0.900353938698 Henry Cohn, 2026, needs more optimization.
5 998 0.900423137276 Henry Cohn, 2026, needs more optimization.
5 999 0.900431347128 Henry Cohn, 2025, needs more optimization.
5 1000 0.900448613272 Henry Cohn, 2026, needs more optimization.
5 1001 0.900513764048 Henry Cohn, 2025, needs more optimization.
5 1002 0.900539735076 Henry Cohn, 2026, needs more optimization.
5 1003 0.900572695383 Henry Cohn, 2026, needs more optimization.
5 1004 0.900586582336 Henry Cohn, 2026, needs more optimization.
5 1006 0.900828745221 Henry Cohn, 2026, needs more optimization.
5 1007 0.900854009714 Henry Cohn, 2025, needs more optimization.
5 1008 0.900860790028 Henry Cohn, 2026, needs more optimization.
5 1009 0.900977984132 Henry Cohn, 2025, needs more optimization.
5 1010 0.900982202691 Henry Cohn, 2026, needs more optimization.
5 1011 0.900985935596 Henry Cohn, 2025, needs more optimization.
5 1012 0.901010944206 Henry Cohn, 2026, needs more optimization.
5 1013 0.901098896278 Henry Cohn, 2025, needs more optimization.
5 1014 0.901116747645 Henry Cohn, 2026, needs more optimization.
5 1015 0.901122877982 Henry Cohn, 2025, needs more optimization.
5 1016 0.901144980530 Henry Cohn, 2026, needs more optimization.
5 1017 0.901213595613 Henry Cohn, 2025, needs more optimization.
5 1018 0.901218963043 Henry Cohn, 2026, needs more optimization.
5 1019 0.901325787568 Henry Cohn, 2025, needs more optimization.
5 1020 0.901329213303 Henry Cohn, 2026, needs more optimization.
5 1021 0.901442156851 Henry Cohn, 2025, needs more optimization.
5 1022 0.901561636441 Henry Cohn, 2026, needs more optimization.
5 1023 0.901639556614 Henry Cohn, 2025, needs more optimization.
5 1024 0.901697490054 Henry Cohn, 2026, needs more optimization.
6 13 0.113079752148 P. G. Adams, A numerical approach to Tamme's problem in Euclidean n-space, Master of Science thesis, Oregon State University, 1997, https://hdl.handle.net/1957/33911.
96⁢x3−36⁢x2−6⁢x+1
6 14 0.132490920324 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
Minimal polynomial listed in plain text data
6 15 0.144948974279 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
20⁢x2+4⁢x−1
6 16 0.171071421043 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
6400⁢x5+960⁢x4−1024⁢x3−32⁢x2+31⁢x−1
6 17 0.183274337024 P. G. Adams, A numerical approach to Tamme's problem in Euclidean n-space, Master of Science thesis, Oregon State University, 1997, https://hdl.handle.net/1957/33911.
400⁢x4+240⁢x3+16⁢x2−8⁢x−1
6 18 0.197812188602 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
784⁢x8−280⁢x7−1191⁢x6+120⁢x5+218⁢x4−62⁢x3−31⁢x2+2⁢x+1
6 19 0.200226025892 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
6 20 0.214285714286 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
14⁢x−3
6 21 0.242852848014 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
6 22 0.248865699460 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
6 23 0.25 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
4⁢x−1
6 24 0.25 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
4⁢x−1
6 25 0.25 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
4⁢x−1
6 26 0.25 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
4⁢x−1
6 27* 0.25 T. Gosset, On the regular and semi-regular figures in space of n dimensions, Messenger Math. 29 (1900), 43–48; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
4⁢x−1
6 28 0.3 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
10⁢x−3
6 29 0.327844830882 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
6 30 0.333157886299 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
6 31 0.333333333334 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
3⁢x−1
6 32 0.333333333334 J. H. van Lint and J. J. Seidel, Equilateral point sets in elliptic geometry, Indag. Math. 28 (1966), 335–348, https://research.tue.nl/en/publications/equilateral-point-sets-in-elliptic-geometry.
3⁢x−1
6 33 0.344948974279 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
20⁢x2−4⁢x−1
6 34 0.346451336111 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
64⁢x5+64⁢x4−76⁢x3+7⁢x2+6⁢x−1
6 35 0.358257569496 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
5⁢x2+x−1
6 36 0.358257569496 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x2+x−1
6 37 0.366623377687 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
64⁢x4+96⁢x3−80⁢x2+16⁢x−1
6 38 0.367688450451 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
7424⁢x8+1280⁢x7−3904⁢x6−768⁢x5+448⁢x4+80⁢x3−1
6 39 0.384936289161 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
6 40 0.386096677606 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
31⁢x4−12⁢x3−14⁢x2+8⁢x−1
6 41 0.389434811673 Henry Cohn, 2023.
6 42 0.390388203203 J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment. Math. 5 (1996), 139–159, https://projecteuclid.org/euclid.em/1047565645; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
4⁢x2+x−1
6 43 0.399773924374 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
1024⁢x9−4096⁢x8−1536⁢x7+1024⁢x6+704⁢x5+64⁢x4−96⁢x3−16⁢x2+4⁢x−1
6 44 0.405666616164 Henry Cohn, 2023.
6 45 0.426943864061 Henry Cohn, 2025.
6 46 0.435705030667 Henry Cohn, 2025.
6 47 0.441277260126 Henry Cohn, 2023.
24⁢x3+16⁢x2−14⁢x+1
6 48 0.443609864234 Henry Cohn, 2025.
6 49 0.446060501890 Henry Cohn, 2023.
6 50 0.446739131277 Henry Cohn, 2023.
58⁢x3−50⁢x2+13⁢x−1
6 51 0.456479386398 Henry Cohn, 2025.
6 52 0.458253528717 Henry Cohn, 2023.
6 53 0.459145031877 Henry Cohn, 2025.
6 54 0.462714285892 Henry Cohn, 2023.
4104⁢x4−216⁢x3−3654⁢x2+1955⁢x−289
6 55 0.472467412878 Henry Cohn, 2024.
6 56 0.475645784548 Henry Cohn, 2023.
33024⁢x6+14848⁢x5−45568⁢x4+5832⁢x3+12257⁢x2−4922⁢x+529
6 57 0.479790821500 Henry Cohn, 2025.
6 58 0.482548584905 Henry Cohn, 2024.
20⁢x2+9⁢x−9
6 59 0.486119746833 Henry Cohn, 2023.
6 60 0.486876290376 Henry Cohn, 2025.
6 61 0.491730182082 Henry Cohn, 2025.
6 62 0.495376595904 Henry Cohn, 2023.
6 63 0.498122491823 Henry Cohn, 2023.
6 64 0.498522963739 Henry Cohn, 2025.
6 65 0.499974913357 Henry Cohn, 2025.
6 66 0.499976896430 Henry Cohn, 2026.
6 67 0.499991659867 Henry Cohn, 2026.
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2⁢x−1
6 73 0.513985952311 Henry Cohn, 2025.
6 74 0.521539568537 Henry Cohn, 2025.
6 75 0.525662331586 Henry Cohn, 2026.
6 76 0.526754953537 Henry Cohn, 2025.
6 77 0.527287929827 Henry Cohn, 2025.
6 78 0.528662896579 Henry Cohn, 2025.
6 79 0.533648501058 Henry Cohn, 2025.
6 80 0.536468893038 Henry Cohn, 2025.
6 81 0.539006300696 Henry Cohn, 2025.
6 82 0.541487958459 Henry Cohn, 2025.
6 83 0.543866459696 Henry Cohn, 2025.
6 84 0.546018230582 Henry Cohn, 2025.
6 85 0.546038397748 Henry Cohn, 2026.
6 86 0.550011129820 Henry Cohn, 2025.
6 87 0.551714767476 Henry Cohn, 2023.
6 88 0.552456735670 Henry Cohn, 2025.
6 89 0.555561660912 Henry Cohn, 2025, needs more optimization.
6 91 0.557603429720 Henry Cohn, 2024.
6 92 0.560971622256 Henry Cohn, 2025.
6 93 0.563013323310 Henry Cohn, 2023.
6 94 0.565350375903 Henry Cohn, 2024.
6 95 0.565789396150 Henry Cohn, 2023.
6 96 0.565950871118 Henry Cohn, 2023.
6 97 0.568133461901 Henry Cohn, 2025.
6 98 0.571167178278 Henry Cohn, 2025.
6 99 0.573881665753 Henry Cohn, 2023.
6 100 0.574916276575 Henry Cohn, 2024.
6 101 0.578331393550 Henry Cohn, 2023.
6 102 0.580736682189 Henry Cohn, 2023, needs more optimization.
6 103 0.583220131624 Henry Cohn, 2024.
6 106 0.583371498649 Henry Cohn, 2026.
6 107 0.583372432432 Henry Cohn, 2026.
6 108 0.584811059741 Henry Cohn, 2026.
6 109 0.585348750770 Henry Cohn, 2026.
6 110 0.585638229827 Henry Cohn, 2025.
6 111 0.585638229827 Henry Cohn, 2026.
6 112 0.585693130025 Henry Cohn, 2026.
6 113 0.586622932873 Henry Cohn, 2025.
6 114 0.588109690133 Henry Cohn, 2023.
6 115 0.596006832892 Henry Cohn, 2025, needs more optimization.
6 116 0.596439214295 Henry Cohn, 2025.
6 117 0.596439359703 Henry Cohn, 2025, needs more optimization.
6 118 0.596439417437 Henry Cohn, 2026.
6 119 0.598424125415 Henry Cohn, 2025.
6 120 0.599174837096 Henry Cohn, 2026.
6 121 0.604468330433 Henry Cohn, 2026, needs more optimization.
6 122 0.606689340567 Henry Cohn, 2025, needs more optimization.
6 123 0.607115797651 Henry Cohn, 2025.
6 124 0.607974063056 Henry Cohn, 2025, needs more optimization.
6 125 0.607974063065 Henry Cohn, 2024, needs more optimization.
6 126 0.610387312456 Henry Cohn, 2026, needs more optimization.
6 127 0.616514741171 Henry Cohn, 2026, needs more optimization.
6 128 0.619107420038 Henry Cohn, 2025.
6 129 0.620224367829 Henry Cohn, 2025.
6 130 0.623555028154 Henry Cohn, 2026, needs more optimization.
6 132 0.624698587774 Henry Cohn, 2026, needs more optimization.
6 133 0.626200672027 Henry Cohn, 2026, needs more optimization.
6 134 0.628628892212 Henry Cohn, 2026, needs more optimization.
6 135 0.630887583786 Henry Cohn, 2025.
6 136 0.631780124977 Henry Cohn, 2026, needs more optimization.
6 137 0.633402294823 Henry Cohn, 2025.
6 138 0.634581559739 Henry Cohn, 2026, needs more optimization.
6 139 0.636180232032 Henry Cohn, 2026, needs more optimization.
6 140 0.637397243455 Henry Cohn, 2026, needs more optimization.
6 141 0.639558404219 Henry Cohn, 2026, needs more optimization.
6 142 0.640016986165 Henry Cohn, 2026, needs more optimization.
6 143 0.641459805982 Henry Cohn, 2026, needs more optimization.
6 144 0.642197637303 Henry Cohn, 2026, needs more optimization.
6 145 0.643736984203 Henry Cohn, 2026, needs more optimization.
6 146 0.644837388208 Henry Cohn, 2026, needs more optimization.
6 147 0.645794121776 Henry Cohn, 2026, needs more optimization.
6 148 0.646695322635 Henry Cohn, 2026, needs more optimization.
6 149 0.648310953648 Henry Cohn, 2026, needs more optimization.
6 150 0.649239191212 Henry Cohn, 2026, needs more optimization.
6 151 0.649913058330 Henry Cohn, 2026, needs more optimization.
6 152 0.651407487635 Henry Cohn, 2026, needs more optimization.
6 153 0.652218453846 Henry Cohn, 2025.
6 154 0.652618605342 Henry Cohn, 2026, needs more optimization.
6 155 0.652686548925 Henry Cohn, 2026, needs more optimization.
6 156 0.653218986491 Henry Cohn, 2026, needs more optimization.
6 157 0.653954713337 Henry Cohn, 2026, needs more optimization.
6 158 0.654673613873 Henry Cohn, 2026, needs more optimization.
6 159 0.654918765162 Henry Cohn, 2026, needs more optimization.
6 160 0.655655023032 Henry Cohn, 2026, needs more optimization.
6 161 0.656360259547 Henry Cohn, 2026, needs more optimization.
6 162 0.657162096688 Henry Cohn, 2026, needs more optimization.
6 163 0.658150909560 Henry Cohn, 2026, needs more optimization.
6 164 0.658813957356 Henry Cohn, 2026, needs more optimization.
6 165 0.659405569935 Henry Cohn, 2026, needs more optimization.
6 166 0.659972001819 Henry Cohn, 2026, needs more optimization.
6 167 0.660494089825 Henry Cohn, 2026, needs more optimization.
6 168 0.660633002772 Henry Cohn, 2026, needs more optimization.
6 169 0.661755325566 Henry Cohn, 2026, needs more optimization.
6 170 0.662756856934 Henry Cohn, 2026, needs more optimization.
6 171 0.664034799222 Henry Cohn, 2026, needs more optimization.
6 172 0.664209295970 Henry Cohn, 2026, needs more optimization.
6 173 0.664534748814 Henry Cohn, 2026, needs more optimization.
6 174 0.664887228221 Henry Cohn, 2026, needs more optimization.
6 175 0.665501021814 Henry Cohn, 2026, needs more optimization.
6 176 0.666136568841 Henry Cohn, 2026, needs more optimization.
6 177 0.667789856480 Henry Cohn, 2026, needs more optimization.
6 178 0.670208134368 Henry Cohn, 2026, needs more optimization.
6 179 0.671285507580 Henry Cohn, 2026, needs more optimization.
6 180 0.671725786395 Henry Cohn, 2026, needs more optimization.
6 181 0.672521263730 Henry Cohn, 2026, needs more optimization.
6 182 0.672898990231 Henry Cohn, 2026, needs more optimization.
6 183 0.673567529777 Henry Cohn, 2026, needs more optimization.
6 184 0.674007349083 Henry Cohn, 2025, needs more optimization.
6 185 0.674430599223 Henry Cohn, 2026, needs more optimization.
6 186 0.674824503468 Henry Cohn, 2026, needs more optimization.
6 187 0.676048363572 Henry Cohn, 2026, needs more optimization.
6 188 0.676645080423 Henry Cohn, 2026, needs more optimization.
6 189 0.677357783496 Henry Cohn, 2026, needs more optimization.
6 190 0.678277877468 Henry Cohn, 2026, needs more optimization.
6 191 0.678622467504 Henry Cohn, 2026, needs more optimization.
6 192 0.679822426017 Henry Cohn, 2026, needs more optimization.
6 193 0.680099334112 Henry Cohn, 2026, needs more optimization.
6 194 0.680909361810 Henry Cohn, 2026, needs more optimization.
6 195 0.681532644969 Henry Cohn, 2026, needs more optimization.
6 196 0.682159746632 Henry Cohn, 2026, needs more optimization.
6 197 0.682766431436 Henry Cohn, 2026, needs more optimization.
6 198 0.683080534618 Henry Cohn, 2026, needs more optimization.
6 199 0.683553802145 Henry Cohn, 2026, needs more optimization.
6 200 0.684465018928 Henry Cohn, 2025, needs more optimization.
6 201 0.684740569115 Henry Cohn, 2026, needs more optimization.
6 202 0.685180223481 Henry Cohn, 2026, needs more optimization.
6 203 0.685546185510 Henry Cohn, 2026, needs more optimization.
6 204 0.686297051198 Henry Cohn, 2026, needs more optimization.
6 205 0.686878507699 Henry Cohn, 2026, needs more optimization.
6 206 0.687366549612 Henry Cohn, 2025, needs more optimization.
6 207 0.687921588908 Henry Cohn, 2026, needs more optimization.
6 208 0.688390951663 Henry Cohn, 2026, needs more optimization.
6 209 0.689397407807 Henry Cohn, 2026, needs more optimization.
6 210 0.690029211034 Henry Cohn, 2026, needs more optimization.
6 211 0.690744229128 Henry Cohn, 2026, needs more optimization.
6 212 0.691274191101 Henry Cohn, 2026, needs more optimization.
6 213 0.691995031842 Henry Cohn, 2026, needs more optimization.
6 214 0.692460410213 Henry Cohn, 2026, needs more optimization.
6 215 0.692862394754 Henry Cohn, 2026, needs more optimization.
6 216 0.693714765332 Henry Cohn, 2026, needs more optimization.
6 217 0.694095583608 Henry Cohn, 2026, needs more optimization.
6 218 0.694916785832 Henry Cohn, 2026, needs more optimization.
6 219 0.695746853480 Henry Cohn, 2026, needs more optimization.
6 220 0.696567490667 Henry Cohn, 2026, needs more optimization.
6 221 0.699055638081 Henry Cohn, 2026, needs more optimization.
6 243 0.7 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
10⁢x−7
6 244 0.704412544995 Henry Cohn, 2026, needs more optimization.
6 245 0.704421457784 Henry Cohn, 2026, needs more optimization.
6 246 0.704428604983 Henry Cohn, 2026, needs more optimization.
6 247 0.704461281269 Henry Cohn, 2026, needs more optimization.
6 248 0.704676584226 Henry Cohn, 2026, needs more optimization.
6 249 0.704738838079 Henry Cohn, 2026, needs more optimization.
6 250 0.705106536843 Henry Cohn, 2025, needs more optimization.
6 251 0.705124811872 Henry Cohn, 2025, needs more optimization.
6 252 0.705192701697 Henry Cohn, 2026, needs more optimization.
6 253 0.705794258515 Henry Cohn, 2025, needs more optimization.
6 255 0.705843588318 Henry Cohn, 2026, needs more optimization.
6 256 0.706169235108 Henry Cohn, 2026, needs more optimization.
6 257 0.706302165620 Henry Cohn, 2026, needs more optimization.
6 258 0.706833900567 Henry Cohn, 2026, needs more optimization.
6 259 0.707211776493 Henry Cohn, 2025, needs more optimization.
6 260 0.707292210716 Henry Cohn, 2026, needs more optimization.
6 261 0.710446151192 Henry Cohn, 2025, needs more optimization.
6 262 0.710476652782 Henry Cohn, 2025, needs more optimization.
6 263 0.710583270955 Henry Cohn, 2026, needs more optimization.
6 264 0.710716541775 Henry Cohn, 2026, needs more optimization.
6 265 0.712521350579 Henry Cohn, 2025, needs more optimization.
6 266 0.712844955170 Henry Cohn, 2026, needs more optimization.
6 267 0.714931955932 Henry Cohn, 2026, needs more optimization.
6 268 0.715225849019 Henry Cohn, 2026, needs more optimization.
6 269 0.715313706808 Henry Cohn, 2026, needs more optimization.
6 270 0.716445862172 Henry Cohn, 2026, needs more optimization.
6 271 0.716615767417 Henry Cohn, 2026, needs more optimization.
6 272 0.717692497225 Henry Cohn, 2026, needs more optimization.
6 274 0.717964292229 Henry Cohn, 2025, needs more optimization.
6 275 0.718472982001 Henry Cohn, 2026, needs more optimization.
6 276 0.719245854451 Henry Cohn, 2026, needs more optimization.
6 277 0.720813612645 Henry Cohn, 2026, needs more optimization.
6 278 0.720823227172 Henry Cohn, 2026, needs more optimization.
6 279 0.721401126539 Henry Cohn, 2026, needs more optimization.
6 280 0.722581820279 Henry Cohn, 2026, needs more optimization.
6 281 0.722624158914 Henry Cohn, 2026, needs more optimization.
6 282 0.723518454655 Henry Cohn, 2025, needs more optimization.
6 283 0.723929075276 Henry Cohn, 2026, needs more optimization.
6 284 0.724648389144 Henry Cohn, 2025, needs more optimization.
6 285 0.724986871185 Henry Cohn, 2026, needs more optimization.
6 286 0.725124817630 Henry Cohn, 2026, needs more optimization.
6 287 0.725353916757 Henry Cohn, 2026, needs more optimization.
6 288 0.726261034203 Henry Cohn, 2026, needs more optimization.
6 289 0.726669077996 Henry Cohn, 2026, needs more optimization.
6 290 0.726809945253 Henry Cohn, 2026, needs more optimization.
6 291 0.728162829923 Henry Cohn, 2025, needs more optimization.
6 292 0.728174504449 Henry Cohn, 2025, needs more optimization.
6 293 0.728704272607 Henry Cohn, 2025, needs more optimization.
6 294 0.729030926219 Henry Cohn, 2025, needs more optimization.
6 295 0.729437652313 Henry Cohn, 2025, needs more optimization.
6 296 0.730290502935 Henry Cohn, 2025, needs more optimization.
6 297 0.731076300664 Henry Cohn, 2025, needs more optimization.
6 298 0.731139671600 Henry Cohn, 2026, needs more optimization.
6 299 0.731510074994 Henry Cohn, 2026, needs more optimization.
6 300 0.732112845366 Henry Cohn, 2025, needs more optimization.
6 301 0.732416678518 Henry Cohn, 2025, needs more optimization.
6 302 0.733154597342 Henry Cohn, 2025, needs more optimization.
6 303 0.733265144419 Henry Cohn, 2025, needs more optimization.
6 304 0.733474326159 Henry Cohn, 2025, needs more optimization.
6 305 0.733794655030 Henry Cohn, 2025, needs more optimization.
6 306 0.733866177993 Henry Cohn, 2025, needs more optimization.
6 307 0.734390329949 Henry Cohn, 2025, needs more optimization.
6 308 0.735132508610 Henry Cohn, 2026, needs more optimization.
6 309 0.735661892248 Henry Cohn, 2025, needs more optimization.
6 310 0.736073358656 Henry Cohn, 2025, needs more optimization.
6 311 0.736181169237 Henry Cohn, 2026, needs more optimization.
6 312 0.736700074960 Henry Cohn, 2025, needs more optimization.
6 313 0.737357322296 Henry Cohn, 2025, needs more optimization.
6 314 0.737761728767 Henry Cohn, 2025, needs more optimization.
6 315 0.737831637343 Henry Cohn, 2025, needs more optimization.
6 316 0.738209850784 Henry Cohn, 2026, needs more optimization.
6 317 0.738613322480 Henry Cohn, 2025, needs more optimization.
6 318 0.739530231283 Henry Cohn, 2025, needs more optimization.
6 319 0.740040267366 Henry Cohn, 2026, needs more optimization.
6 320 0.740195855213 Henry Cohn, 2025, needs more optimization.
6 321 0.740402273601 Henry Cohn, 2026, needs more optimization.
6 322 0.740872947420 Henry Cohn, 2026, needs more optimization.
6 323 0.741323429328 Henry Cohn, 2025, needs more optimization.
6 324 0.741693742410 Henry Cohn, 2026, needs more optimization.
6 325 0.742218586647 Henry Cohn, 2026, needs more optimization.
6 326 0.742456930608 Henry Cohn, 2025, needs more optimization.
6 327 0.742951316911 Henry Cohn, 2025, needs more optimization.
6 328 0.743206035143 Henry Cohn, 2026, needs more optimization.
6 329 0.743917206939 Henry Cohn, 2025, needs more optimization.
6 330 0.744395552873 Henry Cohn, 2026, needs more optimization.
6 331 0.744800502360 Henry Cohn, 2025, needs more optimization.
6 332 0.745075935606 Henry Cohn, 2025, needs more optimization.
6 333 0.745467810779 Henry Cohn, 2025, needs more optimization.
6 334 0.745876428076 Henry Cohn, 2025, needs more optimization.
6 335 0.746518221120 Henry Cohn, 2026, needs more optimization.
6 336 0.746526630978 Henry Cohn, 2026, needs more optimization.
6 340 0.746778829562 Henry Cohn, 2026, needs more optimization.
6 342 0.746790391073 Henry Cohn, 2023, needs more optimization.
6 343 0.748841050044 Henry Cohn, 2025, needs more optimization.
6 344 0.749056432048 Henry Cohn, 2026, needs more optimization.
6 345 0.749265236147 Henry Cohn, 2026, needs more optimization.
6 346 0.749564741696 Henry Cohn, 2025, needs more optimization.
6 347 0.749797304227 Henry Cohn, 2026, needs more optimization.
6 348 0.750331506180 Henry Cohn, 2025, needs more optimization.
6 349 0.750503191071 Henry Cohn, 2025, needs more optimization.
6 350 0.750780551529 Henry Cohn, 2026, needs more optimization.
6 351 0.750837736399 Henry Cohn, 2025, needs more optimization.
6 352 0.751253722010 Henry Cohn, 2025, needs more optimization.
6 353 0.751714863962 Henry Cohn, 2025, needs more optimization.
6 354 0.751805047730 Henry Cohn, 2025, needs more optimization.
6 355 0.751934926381 Henry Cohn, 2025, needs more optimization.
6 356 0.752284354827 Henry Cohn, 2025, needs more optimization.
6 357 0.752897715808 Henry Cohn, 2026, needs more optimization.
6 358 0.752944135015 Henry Cohn, 2025, needs more optimization.
6 359 0.753290360804 Henry Cohn, 2025, needs more optimization.
6 360 0.753398391402 Henry Cohn, 2025, needs more optimization.
6 361 0.753737071365 Henry Cohn, 2025, needs more optimization.
6 362 0.754060455855 Henry Cohn, 2025, needs more optimization.
6 363 0.754391381517 Henry Cohn, 2025, needs more optimization.
6 364 0.754666347797 Henry Cohn, 2025, needs more optimization.
6 365 0.754818502152 Henry Cohn, 2025, needs more optimization.
6 366 0.755036821765 Henry Cohn, 2026, needs more optimization.
6 367 0.755458232833 Henry Cohn, 2025, needs more optimization.
6 368 0.755618078029 Henry Cohn, 2026, needs more optimization.
6 369 0.756134137839 Henry Cohn, 2025, needs more optimization.
6 370 0.756492187511 Henry Cohn, 2025, needs more optimization.
6 371 0.756625060003 Henry Cohn, 2025, needs more optimization.
6 372 0.756759262628 Henry Cohn, 2025, needs more optimization.
6 373 0.757132722236 Henry Cohn, 2025, needs more optimization.
6 374 0.757313417240 Henry Cohn, 2026, needs more optimization.
6 375 0.757922987508 Henry Cohn, 2025, needs more optimization.
6 376 0.757993367495 Henry Cohn, 2025, needs more optimization.
6 377 0.758664541092 Henry Cohn, 2025, needs more optimization.
6 378 0.758717144387 Henry Cohn, 2025, needs more optimization.
6 379 0.758939583890 Ilmari Vahteristo, 2026.
6 380 0.759289338453 Henry Cohn, 2025, needs more optimization.
6 381 0.759421496990 Henry Cohn, 2026, needs more optimization.
6 382 0.759588110302 Henry Cohn, 2025, needs more optimization.
6 383 0.759892829859 Henry Cohn, 2025, needs more optimization.
6 384 0.759900544934 Henry Cohn, 2026, needs more optimization.
6 385 0.760347676343 Henry Cohn, 2025, needs more optimization.
6 386 0.760469383839 Henry Cohn, 2025, needs more optimization.
6 387 0.760835708448 Henry Cohn, 2025, needs more optimization.
6 388 0.761166611751 Henry Cohn, 2026, needs more optimization.
6 389 0.761392923324 Henry Cohn, 2025, needs more optimization.
6 390 0.761779583649 Henry Cohn, 2025, needs more optimization.
6 391 0.761801350661 Henry Cohn, 2025, needs more optimization.
6 392 0.762156311332 Henry Cohn, 2026, needs more optimization.
6 393 0.762160511164 Henry Cohn, 2025, needs more optimization.
6 394 0.762467144423 Henry Cohn, 2025, needs more optimization.
6 395 0.762824595902 Henry Cohn, 2026, needs more optimization.
6 396 0.763226986795 Henry Cohn, 2025, needs more optimization.
6 397 0.763265417521 Henry Cohn, 2025, needs more optimization.
6 398 0.763667586383 Henry Cohn, 2025, needs more optimization.
6 399 0.763778015015 Henry Cohn, 2025, needs more optimization.
6 400 0.764313410189 Henry Cohn, 2025, needs more optimization.
6 401 0.764321098938 Henry Cohn, 2025, needs more optimization.
6 402 0.764359402081 Henry Cohn, 2026, needs more optimization.
6 403 0.764572152690 Henry Cohn, 2025, needs more optimization.
6 404 0.764948720712 Henry Cohn, 2025, needs more optimization.
6 405 0.765119391862 Henry Cohn, 2025, needs more optimization.
6 406 0.765531096457 Henry Cohn, 2026, needs more optimization.
6 407 0.765562373015 Henry Cohn, 2025, needs more optimization.
6 408 0.765843084808 Henry Cohn, 2025, needs more optimization.
6 409 0.765847573501 Henry Cohn, 2025, needs more optimization.
6 410 0.766034682898 Henry Cohn, 2026, needs more optimization.
6 411 0.766428857285 Henry Cohn, 2026, needs more optimization.
6 412 0.766619840406 Henry Cohn, 2025, needs more optimization.
6 413 0.766783053501 Henry Cohn, 2025, needs more optimization.
6 414 0.767103548283 Henry Cohn, 2026, needs more optimization.
6 415 0.767558038199 Henry Cohn, 2025, needs more optimization.
6 416 0.767822571162 Henry Cohn, 2025, needs more optimization.
6 417 0.768110015375 Ilmari Vahteristo, 2026.
6 418 0.768325691504 Henry Cohn, 2025, needs more optimization.
6 419 0.768667400220 Ilmari Vahteristo, 2026.
6 420 0.768700416304 Henry Cohn, 2026, needs more optimization.
6 421 0.768870069376 Henry Cohn, 2025, needs more optimization.
6 422 0.769140912986 Henry Cohn, 2026, needs more optimization.
6 423 0.769380268362 Henry Cohn, 2026, needs more optimization.
6 424 0.769735933377 Henry Cohn, 2026, needs more optimization.
6 425 0.769905701850 Henry Cohn, 2026, needs more optimization.
6 426 0.770200252343 Ilmari Vahteristo, 2026.
6 427 0.770470798880 Henry Cohn, 2025, needs more optimization.
6 428 0.770653463637 Ilmari Vahteristo, 2026.
6 429 0.770681981055 Henry Cohn, 2025, needs more optimization.
6 430 0.770908838569 Henry Cohn, 2026, needs more optimization.
6 431 0.770929384281 Henry Cohn, 2025, needs more optimization.
6 432 0.771241013622 Henry Cohn, 2026, needs more optimization.
6 433 0.771382581330 Henry Cohn, 2025, needs more optimization.
6 434 0.771535594990 Henry Cohn, 2025, needs more optimization.
6 435 0.771885822672 Henry Cohn, 2025, needs more optimization.
6 436 0.771888185017 Henry Cohn, 2026, needs more optimization.
6 437 0.772029819935 Henry Cohn, 2025, needs more optimization.
6 438 0.772265509671 Henry Cohn, 2025, needs more optimization.
6 439 0.772523939817 Henry Cohn, 2025, needs more optimization.
6 440 0.772663149453 Henry Cohn, 2025, needs more optimization.
6 441 0.772955200339 Henry Cohn, 2025, needs more optimization.
6 442 0.773109581137 Henry Cohn, 2026, needs more optimization.
6 443 0.773310557624 Henry Cohn, 2025, needs more optimization.
6 444 0.773776268957 Henry Cohn, 2026, needs more optimization.
6 445 0.773983280335 Henry Cohn, 2025, needs more optimization.
6 446 0.774219246104 Henry Cohn, 2025, needs more optimization.
6 447 0.774236279177 Henry Cohn, 2025, needs more optimization.
6 448 0.774534657349 Henry Cohn, 2026, needs more optimization.
6 449 0.774731477728 Henry Cohn, 2025, needs more optimization.
6 450 0.775058351359 Henry Cohn, 2026, needs more optimization.
6 451 0.775063237723 Henry Cohn, 2026, needs more optimization.
6 452 0.775246412303 Henry Cohn, 2025, needs more optimization.
6 453 0.775432127164 Henry Cohn, 2026, needs more optimization.
6 454 0.775505106768 Henry Cohn, 2025, needs more optimization.
6 455 0.775855579167 Henry Cohn, 2026, needs more optimization.
6 456 0.776068757202 Henry Cohn, 2025, needs more optimization.
6 457 0.776321955413 Henry Cohn, 2025, needs more optimization.
6 458 0.776539559719 Henry Cohn, 2025, needs more optimization.
6 459 0.776803861429 Henry Cohn, 2026, needs more optimization.
6 460 0.776807101274 Henry Cohn, 2025, needs more optimization.
6 461 0.776809166143 Henry Cohn, 2025, needs more optimization.
6 462 0.777196189852 Henry Cohn, 2026, needs more optimization.
6 463 0.777434326346 Henry Cohn, 2025, needs more optimization.
6 464 0.777508700669 Henry Cohn, 2025, needs more optimization.
6 465 0.777692189029 Henry Cohn, 2026, needs more optimization.
6 466 0.777954893493 Henry Cohn, 2026, needs more optimization.
6 467 0.778148493090 Henry Cohn, 2026, needs more optimization.
6 468 0.778287393273 Henry Cohn, 2025, needs more optimization.
6 469 0.778345056785 Henry Cohn, 2026, needs more optimization.
6 470 0.779001228385 Henry Cohn, 2025, needs more optimization.
6 471 0.779024956635 Henry Cohn, 2025, needs more optimization.
6 472 0.779181329561 Henry Cohn, 2025, needs more optimization.
6 473 0.779488936123 Henry Cohn, 2025, needs more optimization.
6 474 0.779739517357 Henry Cohn, 2026, needs more optimization.
6 475 0.779753504424 Henry Cohn, 2025, needs more optimization.
6 476 0.779768569425 Henry Cohn, 2025, needs more optimization.
6 477 0.780128871313 Henry Cohn, 2025, needs more optimization.
6 478 0.780205950103 Henry Cohn, 2025, needs more optimization.
6 479 0.780501205782 Henry Cohn, 2025, needs more optimization.
6 480 0.780553951214 Henry Cohn, 2025, needs more optimization.
6 481 0.780794006151 Henry Cohn, 2026, needs more optimization.
6 482 0.780977289950 Henry Cohn, 2025, needs more optimization.
6 483 0.781178259455 Henry Cohn, 2026, needs more optimization.
6 484 0.781464673023 Henry Cohn, 2026, needs more optimization.
6 485 0.781607451896 Henry Cohn, 2025, needs more optimization.
6 486 0.781666833507 Henry Cohn, 2026, needs more optimization.
6 487 0.782092404018 Henry Cohn, 2025, needs more optimization.
6 488 0.782189214112 Henry Cohn, 2026, needs more optimization.
6 489 0.782411616128 Henry Cohn, 2026, needs more optimization.
6 490 0.782463158072 Henry Cohn, 2025, needs more optimization.
6 491 0.782767005066 Henry Cohn, 2026, needs more optimization.
6 492 0.782865245898 Henry Cohn, 2025, needs more optimization.
6 493 0.783018604741 Henry Cohn, 2026, needs more optimization.
6 494 0.783328089629 Henry Cohn, 2025, needs more optimization.
6 495 0.783396974283 Henry Cohn, 2025, needs more optimization.
6 496 0.783465207879 Henry Cohn, 2026, needs more optimization.
6 497 0.783759592457 Henry Cohn, 2026, needs more optimization.
6 498 0.783946677385 Henry Cohn, 2025, needs more optimization.
6 499 0.783955309086 Henry Cohn, 2025, needs more optimization.
6 500 0.784225819721 Henry Cohn, 2025, needs more optimization.
6 501 0.784506246453 Henry Cohn, 2025, needs more optimization.
6 502 0.784696939909 Henry Cohn, 2025, needs more optimization.
6 503 0.784879873306 Henry Cohn, 2025, needs more optimization.
6 504 0.785043563985 Henry Cohn, 2026, needs more optimization.
6 505 0.785179710994 Henry Cohn, 2026, needs more optimization.
6 506 0.785431882752 Henry Cohn, 2025, needs more optimization.
6 507 0.785540748252 Henry Cohn, 2026, needs more optimization.
6 508 0.785799771003 Henry Cohn, 2026, needs more optimization.
6 509 0.785963085809 Henry Cohn, 2025, needs more optimization.
6 510 0.786078564642 Henry Cohn, 2025, needs more optimization.
6 511 0.786344662388 Henry Cohn, 2025, needs more optimization.
6 512 0.786379684678 Henry Cohn, 2026, needs more optimization.
6 513 0.786463332303 Henry Cohn, 2026, needs more optimization.
6 514 0.786699853689 Henry Cohn, 2026, needs more optimization.
6 515 0.786913884715 Henry Cohn, 2025, needs more optimization.
6 516 0.787047171505 Henry Cohn, 2026, needs more optimization.
6 517 0.787230377399 Henry Cohn, 2026, needs more optimization.
6 518 0.787272798145 Henry Cohn, 2025, needs more optimization.
6 519 0.787318272676 Henry Cohn, 2025, needs more optimization.
6 520 0.787617124479 Henry Cohn, 2025, needs more optimization.
6 521 0.787734926114 Henry Cohn, 2025, needs more optimization.
6 522 0.788137976651 Henry Cohn, 2025, needs more optimization.
6 523 0.788156267395 Henry Cohn, 2025, needs more optimization.
6 524 0.788441800907 Henry Cohn, 2026, needs more optimization.
6 525 0.788608388669 Henry Cohn, 2025, needs more optimization.
6 526 0.788709148657 Henry Cohn, 2025, needs more optimization.
6 527 0.788874161694 Henry Cohn, 2026, needs more optimization.
6 528 0.788926543638 Henry Cohn, 2026, needs more optimization.
6 529 0.789134700458 Henry Cohn, 2025, needs more optimization.
6 530 0.789414807102 Henry Cohn, 2025, needs more optimization.
6 531 0.789428246829 Henry Cohn, 2026, needs more optimization.
6 532 0.789787457345 Henry Cohn, 2026, needs more optimization.
6 533 0.789792757309 Henry Cohn, 2025, needs more optimization.
6 534 0.789817192244 Henry Cohn, 2025, needs more optimization.
6 535 0.790045702885 Henry Cohn, 2025, needs more optimization.
6 536 0.790080666571 Henry Cohn, 2025, needs more optimization.
6 537 0.790456481764 Henry Cohn, 2026, needs more optimization.
6 538 0.790512511145 Henry Cohn, 2026, needs more optimization.
6 539 0.790575573190 Henry Cohn, 2025, needs more optimization.
6 540 0.790802834220 Henry Cohn, 2026, needs more optimization.
6 541 0.790905992923 Henry Cohn, 2026, needs more optimization.
6 542 0.790912425048 Henry Cohn, 2025, needs more optimization.
6 543 0.791109702429 Henry Cohn, 2025, needs more optimization.
6 544 0.791482114125 Henry Cohn, 2026, needs more optimization.
6 545 0.791558205412 Henry Cohn, 2026, needs more optimization.
6 546 0.791799721623 Henry Cohn, 2025, needs more optimization.
6 547 0.791817853845 Henry Cohn, 2025, needs more optimization.
6 548 0.792007169007 Henry Cohn, 2026, needs more optimization.
6 549 0.792120458535 Henry Cohn, 2025, needs more optimization.
6 550 0.792413480597 Henry Cohn, 2026, needs more optimization.
6 551 0.792571287759 Henry Cohn, 2025, needs more optimization.
6 552 0.792575911224 Henry Cohn, 2026, needs more optimization.
6 553 0.792720237063 Henry Cohn, 2025, needs more optimization.
6 554 0.792991123280 Henry Cohn, 2025, needs more optimization.
6 555 0.793030377786 Henry Cohn, 2025, needs more optimization.
6 556 0.793345560359 Henry Cohn, 2025, needs more optimization.
6 557 0.793375623664 Henry Cohn, 2025, needs more optimization.
6 558 0.793392931595 Henry Cohn, 2026, needs more optimization.
6 559 0.793540032966 Henry Cohn, 2026, needs more optimization.
6 560 0.793970939934 Henry Cohn, 2026, needs more optimization.
6 561 0.793997720863 Henry Cohn, 2025, needs more optimization.
6 562 0.793999096351 Henry Cohn, 2025, needs more optimization.
6 563 0.794253599934 Henry Cohn, 2025, needs more optimization.
6 564 0.794345967712 Henry Cohn, 2025, needs more optimization.
6 565 0.794514240296 Henry Cohn, 2025, needs more optimization.
6 566 0.794720999866 Henry Cohn, 2025, needs more optimization.
6 567 0.794822227717 Henry Cohn, 2026, needs more optimization.
6 568 0.795027686258 Henry Cohn, 2026, needs more optimization.
6 569 0.795033176405 Henry Cohn, 2026, needs more optimization.
6 570 0.795265951322 Henry Cohn, 2026, needs more optimization.
6 571 0.795288705125 Henry Cohn, 2025, needs more optimization.
6 572 0.795516409345 Henry Cohn, 2025, needs more optimization.
6 573 0.795829156946 Henry Cohn, 2025, needs more optimization.
6 574 0.795900175913 Henry Cohn, 2025, needs more optimization.
6 575 0.795904568008 Henry Cohn, 2025, needs more optimization.
6 576 0.796101080809 Henry Cohn, 2025, needs more optimization.
6 577 0.796256548729 Henry Cohn, 2025, needs more optimization.
6 578 0.796571670123 Henry Cohn, 2025, needs more optimization.
6 579 0.796576792514 Henry Cohn, 2026, needs more optimization.
6 580 0.796751653475 Henry Cohn, 2025, needs more optimization.
6 581 0.796786785592 Henry Cohn, 2026, needs more optimization.
6 582 0.797057202471 Henry Cohn, 2025, needs more optimization.
6 583 0.797104811578 Henry Cohn, 2025, needs more optimization.
6 584 0.797356665470 Henry Cohn, 2026, needs more optimization.
6 585 0.797384718954 Henry Cohn, 2025, needs more optimization.
6 586 0.797385241881 Henry Cohn, 2026, needs more optimization.
6 587 0.797603948018 Henry Cohn, 2025, needs more optimization.
6 588 0.797789322431 Henry Cohn, 2026, needs more optimization.
6 589 0.797840114335 Henry Cohn, 2026, needs more optimization.
6 590 0.798162548924 Henry Cohn, 2026, needs more optimization.
6 591 0.798166091649 Henry Cohn, 2025, needs more optimization.
6 592 0.798376791335 Henry Cohn, 2025, needs more optimization.
6 593 0.798472384327 Henry Cohn, 2025, needs more optimization.
6 594 0.798669532087 Henry Cohn, 2026, needs more optimization.
6 595 0.798805187978 Henry Cohn, 2025, needs more optimization.
6 596 0.799063819653 Henry Cohn, 2026, needs more optimization.
6 597 0.799214553851 Henry Cohn, 2025, needs more optimization.
6 598 0.799240654751 Henry Cohn, 2026, needs more optimization.
6 599 0.799406794187 Henry Cohn, 2025, needs more optimization.
6 600 0.799541345677 Henry Cohn, 2026, needs more optimization.
6 601 0.799696542620 Henry Cohn, 2025, needs more optimization.
6 602 0.799818854650 Henry Cohn, 2026, needs more optimization.
6 603 0.799927083241 Henry Cohn, 2025, needs more optimization.
6 604 0.800237726072 Henry Cohn, 2025, needs more optimization.
6 605 0.800238223191 Henry Cohn, 2025, needs more optimization.
6 606 0.800239423949 Henry Cohn, 2025, needs more optimization.
6 607 0.800492441363 Henry Cohn, 2025, needs more optimization.
6 608 0.800495024091 Henry Cohn, 2026, needs more optimization.
6 609 0.800688709880 Henry Cohn, 2025, needs more optimization.
6 610 0.801072650459 Henry Cohn, 2025, needs more optimization.
6 611 0.801085375103 Henry Cohn, 2026, needs more optimization.
6 612 0.801133000500 Henry Cohn, 2025, needs more optimization.
6 613 0.801192982451 Henry Cohn, 2025, needs more optimization.
6 614 0.801486649069 Henry Cohn, 2026, needs more optimization.
6 615 0.801487334924 Henry Cohn, 2025, needs more optimization.
6 616 0.801657461132 Henry Cohn, 2026, needs more optimization.
6 617 0.801682559413 Henry Cohn, 2026, needs more optimization.
6 618 0.801908204381 Henry Cohn, 2026, needs more optimization.
6 619 0.801914036391 Henry Cohn, 2026, needs more optimization.
6 620 0.802028436564 Henry Cohn, 2026, needs more optimization.
6 621 0.802209048142 Henry Cohn, 2026, needs more optimization.
6 622 0.802454074297 Henry Cohn, 2025, needs more optimization.
6 623 0.802568688111 Henry Cohn, 2025, needs more optimization.
6 624 0.802580355221 Henry Cohn, 2026, needs more optimization.
6 625 0.802875169852 Henry Cohn, 2025, needs more optimization.
6 626 0.802899751488 Henry Cohn, 2026, needs more optimization.
6 627 0.802921218541 Henry Cohn, 2025, needs more optimization.
6 628 0.803035532929 Henry Cohn, 2026, needs more optimization.
6 629 0.803299590474 Henry Cohn, 2026, needs more optimization.
6 630 0.803301323863 Henry Cohn, 2026, needs more optimization.
6 631 0.803487382574 Henry Cohn, 2025, needs more optimization.
6 632 0.803728175116 Henry Cohn, 2026, needs more optimization.
6 633 0.803849473735 Henry Cohn, 2026, needs more optimization.
6 634 0.804007465348 Henry Cohn, 2026, needs more optimization.
6 635 0.804025542024 Henry Cohn, 2025, needs more optimization.
6 636 0.804180065316 Henry Cohn, 2026, needs more optimization.
6 637 0.804238749445 Henry Cohn, 2026, needs more optimization.
6 638 0.804384859272 Henry Cohn, 2025, needs more optimization.
6 639 0.804386938080 Henry Cohn, 2026, needs more optimization.
6 640 0.804616355202 Henry Cohn, 2025, needs more optimization.
6 641 0.804666298456 Henry Cohn, 2025, needs more optimization.
6 642 0.804672578592 Henry Cohn, 2025, needs more optimization.
6 643 0.804842333605 Henry Cohn, 2026, needs more optimization.
6 644 0.805068138518 Henry Cohn, 2026, needs more optimization.
6 645 0.805285069869 Henry Cohn, 2025, needs more optimization.
6 646 0.805384911647 Henry Cohn, 2025, needs more optimization.
6 647 0.805448187462 Henry Cohn, 2025, needs more optimization.
6 648 0.805456820919 Henry Cohn, 2025, needs more optimization.
6 649 0.805642092642 Henry Cohn, 2025, needs more optimization.
6 650 0.805658850314 Henry Cohn, 2025, needs more optimization.
6 651 0.805913789108 Henry Cohn, 2026, needs more optimization.
6 652 0.805952437252 Henry Cohn, 2026, needs more optimization.
6 653 0.806116288247 Henry Cohn, 2026, needs more optimization.
6 654 0.806370880524 Henry Cohn, 2025, needs more optimization.
6 655 0.806375912850 Henry Cohn, 2025, needs more optimization.
6 656 0.806422253369 Henry Cohn, 2026, needs more optimization.
6 657 0.806640579298 Henry Cohn, 2025, needs more optimization.
6 658 0.806679762038 Henry Cohn, 2025, needs more optimization.
6 659 0.806730375136 Henry Cohn, 2025, needs more optimization.
6 660 0.806757030490 Henry Cohn, 2025, needs more optimization.
6 661 0.806983357269 Henry Cohn, 2025, needs more optimization.
6 662 0.807247874962 Henry Cohn, 2025, needs more optimization.
6 663 0.807373630299 Henry Cohn, 2026, needs more optimization.
6 664 0.807378892261 Henry Cohn, 2026, needs more optimization.
6 665 0.807624736629 Henry Cohn, 2026, needs more optimization.
6 666 0.807660969307 Henry Cohn, 2026, needs more optimization.
6 667 0.807795326218 Henry Cohn, 2025, needs more optimization.
6 668 0.807828789748 Henry Cohn, 2025, needs more optimization.
6 669 0.807833607483 Henry Cohn, 2025, needs more optimization.
6 670 0.807898038068 Henry Cohn, 2026, needs more optimization.
6 671 0.808077665747 Henry Cohn, 2026, needs more optimization.
6 672 0.808175676168 Henry Cohn, 2026, needs more optimization.
6 673 0.808414765330 Henry Cohn, 2025, needs more optimization.
6 674 0.808465382532 Henry Cohn, 2026, needs more optimization.
6 676 0.808770309220 Henry Cohn, 2026, needs more optimization.
6 677 0.808946782452 Henry Cohn, 2025, needs more optimization.
6 678 0.809095726889 Henry Cohn, 2026, needs more optimization.
6 679 0.809105555259 Henry Cohn, 2025, needs more optimization.
6 680 0.809285168486 Henry Cohn, 2025, needs more optimization.
6 681 0.809550813598 Henry Cohn, 2025, needs more optimization.
6 682 0.809556610555 Henry Cohn, 2026, needs more optimization.
6 683 0.809593568170 Henry Cohn, 2025, needs more optimization.
6 684 0.809809729757 Henry Cohn, 2026, needs more optimization.
6 685 0.809815681557 Henry Cohn, 2025, needs more optimization.
6 686 0.809957609025 Henry Cohn, 2026, needs more optimization.
6 687 0.809987501148 Henry Cohn, 2026, needs more optimization.
6 688 0.810216131855 Henry Cohn, 2025, needs more optimization.
6 689 0.810286164813 Henry Cohn, 2025, needs more optimization.
6 690 0.810404495670 Henry Cohn, 2025, needs more optimization.
6 691 0.810680318644 Henry Cohn, 2025, needs more optimization.
6 692 0.810691458399 Henry Cohn, 2026, needs more optimization.
6 693 0.810692518870 Henry Cohn, 2026, needs more optimization.
6 694 0.810880398447 Henry Cohn, 2026, needs more optimization.
6 695 0.810952995250 Henry Cohn, 2025, needs more optimization.
6 696 0.811134509113 Henry Cohn, 2026, needs more optimization.
6 697 0.811178575942 Henry Cohn, 2026, needs more optimization.
6 698 0.811436541795 Henry Cohn, 2025, needs more optimization.
6 699 0.811556195073 Henry Cohn, 2025, needs more optimization.
6 700 0.811692885419 Henry Cohn, 2026, needs more optimization.
6 701 0.811698518362 Henry Cohn, 2026, needs more optimization.
6 702 0.811787077923 Henry Cohn, 2025, needs more optimization.
6 703 0.811896779748 Henry Cohn, 2026, needs more optimization.
6 704 0.811933453698 Henry Cohn, 2026, needs more optimization.
6 705 0.812056196050 Henry Cohn, 2026, needs more optimization.
6 706 0.812327856122 Henry Cohn, 2026, needs more optimization.
6 707 0.812337723232 Henry Cohn, 2025, needs more optimization.
6 708 0.812521323092 Henry Cohn, 2025, needs more optimization.
6 709 0.812709123718 Henry Cohn, 2026, needs more optimization.
6 710 0.812869067662 Henry Cohn, 2026, needs more optimization.
6 711 0.812870939378 Henry Cohn, 2025, needs more optimization.
6 712 0.812909766290 Henry Cohn, 2026, needs more optimization.
6 713 0.813168514782 Henry Cohn, 2025, needs more optimization.
6 714 0.813189998744 Henry Cohn, 2026, needs more optimization.
6 715 0.813306799649 Henry Cohn, 2025, needs more optimization.
6 716 0.813312306830 Henry Cohn, 2025, needs more optimization.
6 717 0.813340180925 Henry Cohn, 2025, needs more optimization.
6 718 0.813642939265 Henry Cohn, 2026, needs more optimization.
6 719 0.813647808802 Henry Cohn, 2025, needs more optimization.
6 720 0.813677877521 Henry Cohn, 2026, needs more optimization.
6 721 0.813962266975 Henry Cohn, 2025, needs more optimization.
6 722 0.814008585494 Henry Cohn, 2025, needs more optimization.
6 723 0.814032728403 Henry Cohn, 2026, needs more optimization.
6 724 0.814066976477 Henry Cohn, 2026, needs more optimization.
6 725 0.814205535670 Henry Cohn, 2026, needs more optimization.
6 726 0.814326606162 Henry Cohn, 2026, needs more optimization.
6 727 0.814502502478 Henry Cohn, 2026, needs more optimization.
6 728 0.814503288797 Henry Cohn, 2025, needs more optimization.
6 729 0.814570219480 Henry Cohn, 2026, needs more optimization.
6 730 0.814691836372 Henry Cohn, 2026, needs more optimization.
6 731 0.814856583331 Henry Cohn, 2026, needs more optimization.
6 732 0.814941616114 Henry Cohn, 2026, needs more optimization.
6 733 0.815064953607 Henry Cohn, 2025, needs more optimization.
6 734 0.815069220671 Henry Cohn, 2026, needs more optimization.
6 735 0.815129595166 Henry Cohn, 2025, needs more optimization.
6 736 0.815223603952 Henry Cohn, 2025, needs more optimization.
6 737 0.815682268478 Henry Cohn, 2026, needs more optimization.
6 738 0.815693468417 Henry Cohn, 2026, needs more optimization.
6 739 0.815709376578 Henry Cohn, 2025, needs more optimization.
6 740 0.815877414246 Henry Cohn, 2026, needs more optimization.
6 741 0.815898132570 Henry Cohn, 2025, needs more optimization.
6 742 0.816035439694 Henry Cohn, 2026, needs more optimization.
6 743 0.816066086302 Henry Cohn, 2025, needs more optimization.
6 744 0.816072924951 Henry Cohn, 2026, needs more optimization.
6 745 0.816297758800 Henry Cohn, 2025, needs more optimization.
6 746 0.816305246119 Henry Cohn, 2026, needs more optimization.
6 747 0.816590719307 Henry Cohn, 2026, needs more optimization.
6 748 0.816629818356 Henry Cohn, 2025, needs more optimization.
6 749 0.816636310815 Henry Cohn, 2025, needs more optimization.
6 750 0.816834403280 Henry Cohn, 2026, needs more optimization.
6 751 0.816988092892 Henry Cohn, 2026, needs more optimization.
6 752 0.817000737748 Henry Cohn, 2026, needs more optimization.
6 753 0.817252063848 Henry Cohn, 2025, needs more optimization.
6 754 0.817260199019 Henry Cohn, 2025, needs more optimization.
6 755 0.817289678208 Henry Cohn, 2026, needs more optimization.
6 756 0.817435527872 Henry Cohn, 2026, needs more optimization.
6 757 0.817476590341 Henry Cohn, 2025, needs more optimization.
6 758 0.817494710876 Henry Cohn, 2026, needs more optimization.
6 759 0.817679682538 Henry Cohn, 2025, needs more optimization.
6 760 0.817728595799 Henry Cohn, 2026, needs more optimization.
6 761 0.817738637151 Henry Cohn, 2026, needs more optimization.
6 762 0.818009280002 Henry Cohn, 2025, needs more optimization.
6 763 0.818126943364 Henry Cohn, 2026, needs more optimization.
6 764 0.818293022730 Henry Cohn, 2026, needs more optimization.
6 765 0.818387391667 Henry Cohn, 2025, needs more optimization.
6 766 0.818390063895 Henry Cohn, 2026, needs more optimization.
6 767 0.818394454662 Henry Cohn, 2025, needs more optimization.
6 768 0.818596596606 Henry Cohn, 2025, needs more optimization.
6 769 0.818775965803 Henry Cohn, 2025, needs more optimization.
6 770 0.818805061007 Henry Cohn, 2026, needs more optimization.
6 771 0.818923267989 Henry Cohn, 2026, needs more optimization.
6 772 0.818932450167 Henry Cohn, 2026, needs more optimization.
6 773 0.818970769208 Henry Cohn, 2025, needs more optimization.
6 774 0.819128780864 Henry Cohn, 2026, needs more optimization.
6 775 0.819130040801 Henry Cohn, 2026, needs more optimization.
6 776 0.819373850853 Henry Cohn, 2026, needs more optimization.
6 777 0.819410314136 Henry Cohn, 2025, needs more optimization.
6 778 0.819549833203 Henry Cohn, 2025, needs more optimization.
6 779 0.819551772387 Henry Cohn, 2026, needs more optimization.
6 780 0.819703678444 Henry Cohn, 2026, needs more optimization.
6 781 0.819710578070 Henry Cohn, 2026, needs more optimization.
6 782 0.819732926480 Henry Cohn, 2026, needs more optimization.
6 783 0.819933707254 Henry Cohn, 2025, needs more optimization.
6 784 0.819960428163 Henry Cohn, 2026, needs more optimization.
6 785 0.820143659869 Henry Cohn, 2025, needs more optimization.
6 786 0.820162296273 Henry Cohn, 2026, needs more optimization.
6 787 0.820192193425 Henry Cohn, 2026, needs more optimization.
6 788 0.820407823502 Henry Cohn, 2026, needs more optimization.
6 789 0.820418485236 Henry Cohn, 2025, needs more optimization.
6 790 0.820541743786 Henry Cohn, 2026, needs more optimization.
6 791 0.820646161966 Henry Cohn, 2026, needs more optimization.
6 792 0.820801628820 Henry Cohn, 2026, needs more optimization.
6 793 0.820847663795 Henry Cohn, 2025, needs more optimization.
6 794 0.820992944116 Henry Cohn, 2026, needs more optimization.
6 795 0.820998941353 Henry Cohn, 2025, needs more optimization.
6 796 0.821019788207 Henry Cohn, 2025, needs more optimization.
6 797 0.821162357325 Henry Cohn, 2026, needs more optimization.
6 798 0.821167863597 Henry Cohn, 2026, needs more optimization.
6 799 0.821271329935 Henry Cohn, 2025, needs more optimization.
6 800 0.821599446854 Henry Cohn, 2025, needs more optimization.
6 801 0.821655585342 Henry Cohn, 2025, needs more optimization.
6 802 0.821670709678 Henry Cohn, 2026, needs more optimization.
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6 805 0.821921704628 Henry Cohn, 2025, needs more optimization.
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6 807 0.822127138753 Henry Cohn, 2025, needs more optimization.
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6 810 0.822299924242 Henry Cohn, 2025, needs more optimization.
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6 812 0.822493820161 Henry Cohn, 2026, needs more optimization.
6 813 0.822714297203 Henry Cohn, 2025, needs more optimization.
6 814 0.822717523257 Henry Cohn, 2026, needs more optimization.
6 815 0.822810732997 Henry Cohn, 2025, needs more optimization.
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6 820 0.823199035966 Henry Cohn, 2026, needs more optimization.
6 821 0.823458312032 Henry Cohn, 2025, needs more optimization.
6 822 0.823659438728 Henry Cohn, 2026, needs more optimization.
6 824 0.823661404172 Henry Cohn, 2025, needs more optimization.
6 825 0.823727831164 Henry Cohn, 2025, needs more optimization.
6 826 0.823991086599 Henry Cohn, 2026, needs more optimization.
6 827 0.823998838954 Henry Cohn, 2025, needs more optimization.
6 828 0.824000600074 Henry Cohn, 2026, needs more optimization.
6 829 0.824087347346 Henry Cohn, 2026, needs more optimization.
6 830 0.824248007756 Henry Cohn, 2026, needs more optimization.
6 831 0.824253060781 Henry Cohn, 2025, needs more optimization.
6 832 0.824405563460 Henry Cohn, 2026, needs more optimization.
6 833 0.824413825655 Henry Cohn, 2025, needs more optimization.
6 834 0.824560460920 Henry Cohn, 2025, needs more optimization.
6 835 0.824562867216 Henry Cohn, 2025, needs more optimization.
6 836 0.824565043044 Henry Cohn, 2025, needs more optimization.
6 837 0.824857490202 Henry Cohn, 2025, needs more optimization.
6 838 0.824860456156 Henry Cohn, 2026, needs more optimization.
6 839 0.824886179725 Henry Cohn, 2026, needs more optimization.
6 840 0.824920182114 Henry Cohn, 2025, needs more optimization.
6 841 0.825001746346 Henry Cohn, 2025, needs more optimization.
6 842 0.825315243286 Henry Cohn, 2026, needs more optimization.
6 843 0.825320807229 Henry Cohn, 2025, needs more optimization.
6 844 0.825332142790 Henry Cohn, 2026, needs more optimization.
6 845 0.825431145892 Henry Cohn, 2025, needs more optimization.
6 846 0.825565311431 Henry Cohn, 2026, needs more optimization.
6 847 0.825579490995 Henry Cohn, 2025, needs more optimization.
6 848 0.825586029457 Henry Cohn, 2026, needs more optimization.
6 849 0.825841722374 Henry Cohn, 2025, needs more optimization.
6 850 0.825859233687 Henry Cohn, 2026, needs more optimization.
6 851 0.825868206288 Henry Cohn, 2026, needs more optimization.
6 852 0.826024374941 Henry Cohn, 2026, needs more optimization.
6 853 0.826141690504 Henry Cohn, 2025, needs more optimization.
6 854 0.826367084565 Henry Cohn, 2026, needs more optimization.
6 855 0.826400472648 Henry Cohn, 2025, needs more optimization.
6 856 0.826415296291 Henry Cohn, 2026, needs more optimization.
6 857 0.826652046639 Henry Cohn, 2025, needs more optimization.
6 858 0.826659628926 Henry Cohn, 2025, needs more optimization.
6 859 0.826687113923 Henry Cohn, 2026, needs more optimization.
6 860 0.826841472698 Henry Cohn, 2026, needs more optimization.
6 861 0.826932469101 Henry Cohn, 2026, needs more optimization.
6 862 0.826936718325 Henry Cohn, 2026, needs more optimization.
6 863 0.827096118447 Henry Cohn, 2025, needs more optimization.
6 864 0.827100003459 Henry Cohn, 2026, needs more optimization.
6 865 0.827296940286 Henry Cohn, 2026, needs more optimization.
6 867 0.827303375728 Henry Cohn, 2025, needs more optimization.
6 868 0.827394189128 Henry Cohn, 2026, needs more optimization.
6 869 0.827401797850 Henry Cohn, 2026, needs more optimization.
6 870 0.827591086516 Henry Cohn, 2026, needs more optimization.
6 871 0.827597158369 Henry Cohn, 2025, needs more optimization.
6 872 0.827728271232 Henry Cohn, 2026, needs more optimization.
6 873 0.827729680529 Henry Cohn, 2026, needs more optimization.
6 874 0.827730794125 Henry Cohn, 2025, needs more optimization.
6 875 0.827737392377 Henry Cohn, 2025, needs more optimization.
6 876 0.827801485706 Henry Cohn, 2026, needs more optimization.
6 877 0.827866203405 Henry Cohn, 2026, needs more optimization.
6 878 0.827995146225 Henry Cohn, 2026, needs more optimization.
6 880 0.828018048100 Henry Cohn, 2026, needs more optimization.
6 882 0.828043374383 Henry Cohn, 2026, needs more optimization.
6 883 0.828099087083 Henry Cohn, 2025, needs more optimization.
6 884 0.828212504038 Henry Cohn, 2026, needs more optimization.
6 885 0.828338428446 Henry Cohn, 2026, needs more optimization.
6 886 0.828367158085 Henry Cohn, 2026, needs more optimization.
6 887 0.828500110788 Henry Cohn, 2025, needs more optimization.
6 888 0.828533748457 Henry Cohn, 2026, needs more optimization.
6 890 0.828644258996 Henry Cohn, 2025, needs more optimization.
6 891 0.828695697577 Henry Cohn, 2025, needs more optimization.
6 892 0.828880658446 Henry Cohn, 2026, needs more optimization.
6 894 0.828882968640 Henry Cohn, 2026, needs more optimization.
6 895 0.828942339148 Henry Cohn, 2026, needs more optimization.
6 896 0.828942922823 Henry Cohn, 2025, needs more optimization.
6 897 0.829140202323 Henry Cohn, 2025, needs more optimization.
6 898 0.829142880376 Henry Cohn, 2025, needs more optimization.
6 899 0.829153915719 Henry Cohn, 2025, needs more optimization.
6 900 0.829310619521 Henry Cohn, 2026, needs more optimization.
6 901 0.829419331220 Henry Cohn, 2026, needs more optimization.
6 902 0.829425911396 Henry Cohn, 2026, needs more optimization.
6 904 0.829628240514 Henry Cohn, 2026, needs more optimization.
6 905 0.829701077326 Henry Cohn, 2025, needs more optimization.
6 906 0.829812045947 Henry Cohn, 2025, needs more optimization.
6 907 0.829817198209 Henry Cohn, 2025, needs more optimization.
6 908 0.829818655010 Henry Cohn, 2025, needs more optimization.
6 909 0.830020033127 Henry Cohn, 2026, needs more optimization.
6 910 0.830022358121 Henry Cohn, 2026, needs more optimization.
6 911 0.830065610631 Henry Cohn, 2025, needs more optimization.
6 912 0.830113517537 Henry Cohn, 2026, needs more optimization.
6 913 0.830239845292 Henry Cohn, 2026, needs more optimization.
6 914 0.830242519417 Henry Cohn, 2025, needs more optimization.
6 916 0.830521683842 Henry Cohn, 2026, needs more optimization.
6 917 0.830522878283 Henry Cohn, 2025, needs more optimization.
6 918 0.830527013915 Henry Cohn, 2025, needs more optimization.
6 919 0.830527776902 Henry Cohn, 2025, needs more optimization.
6 920 0.830717981265 Henry Cohn, 2026, needs more optimization.
6 921 0.830738180489 Henry Cohn, 2025, needs more optimization.
6 922 0.830829231774 Henry Cohn, 2025, needs more optimization.
6 923 0.830840743540 Henry Cohn, 2025, needs more optimization.
6 924 0.830903672293 Henry Cohn, 2026, needs more optimization.
6 925 0.830906862451 Henry Cohn, 2025, needs more optimization.
6 926 0.830908268155 Henry Cohn, 2025, needs more optimization.
6 928 0.831284349465 Henry Cohn, 2025, needs more optimization.
6 929 0.831287055099 Henry Cohn, 2025, needs more optimization.
6 930 0.831324563680 Henry Cohn, 2026, needs more optimization.
6 932 0.831470102843 Henry Cohn, 2026, needs more optimization.
6 934 0.831471312652 Henry Cohn, 2026, needs more optimization.
6 936 0.831503858491 Henry Cohn, 2026, needs more optimization.
6 937 0.831654977354 Henry Cohn, 2025, needs more optimization.
6 938 0.831657240242 Henry Cohn, 2025, needs more optimization.
6 939 0.831778720014 Henry Cohn, 2026, needs more optimization.
6 940 0.831799691532 Henry Cohn, 2026, needs more optimization.
6 941 0.831803415016 Henry Cohn, 2025, needs more optimization.
6 942 0.831841531793 Henry Cohn, 2026, needs more optimization.
6 944 0.831997404175 Henry Cohn, 2026, needs more optimization.
6 945 0.831997660390 Henry Cohn, 2026, needs more optimization.
6 946 0.831998896870 Henry Cohn, 2026, needs more optimization.
6 947 0.832020842073 Henry Cohn, 2026, needs more optimization.
6 948 0.832138138234 Henry Cohn, 2025, needs more optimization.
6 950 0.832149915545 Henry Cohn, 2026, needs more optimization.
6 951 0.832288455846 Henry Cohn, 2026, needs more optimization.
6 952 0.832294478981 Henry Cohn, 2026, needs more optimization.
6 953 0.832310934537 Henry Cohn, 2026, needs more optimization.
6 954 0.832417246251 Henry Cohn, 2026, needs more optimization.
6 956 0.832433305929 Henry Cohn, 2026, needs more optimization.
6 957 0.832443618756 Henry Cohn, 2025, needs more optimization.
6 958 0.832590542539 Henry Cohn, 2026, needs more optimization.
6 959 0.832608439140 Henry Cohn, 2025, needs more optimization.
6 960 0.832608515714 Henry Cohn, 2025, needs more optimization.
6 961 0.832622827750 Henry Cohn, 2026, needs more optimization.
6 962 0.832768207726 Henry Cohn, 2026, needs more optimization.
6 964 0.832772805190 Henry Cohn, 2026, needs more optimization.
6 965 0.832786351085 Henry Cohn, 2025, needs more optimization.
6 966 0.832897436776 Henry Cohn, 2026, needs more optimization.
6 967 0.832901388916 Henry Cohn, 2025, needs more optimization.
6 968 0.832904729760 Henry Cohn, 2026, needs more optimization.
6 969 0.832918121401 Henry Cohn, 2025, needs more optimization.
6 990 0.833333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
6⁢x−5
6 991 0.835257411625 Henry Cohn, 2026, needs more optimization.
6 992 0.836344602402 Henry Cohn, 2026, needs more optimization.
6 993 0.836365663324 Henry Cohn, 2025, needs more optimization.
6 994 0.836412974463 Henry Cohn, 2026, needs more optimization.
6 995 0.836413523076 Henry Cohn, 2025, needs more optimization.
6 996 0.836586134983 Henry Cohn, 2025, needs more optimization.
6 997 0.836735501990 Henry Cohn, 2026, needs more optimization.
6 998 0.836761414944 Henry Cohn, 2026, needs more optimization.
6 999 0.836916042999 Henry Cohn, 2025, needs more optimization.
6 1000 0.836920990870 Henry Cohn, 2026, needs more optimization.
6 1001 0.836925063933 Henry Cohn, 2026, needs more optimization.
6 1002 0.836953091035 Henry Cohn, 2026, needs more optimization.
6 1004 0.837120788733 Henry Cohn, 2025, needs more optimization.
6 1006 0.837374559607 Henry Cohn, 2026, needs more optimization.
6 1007 0.837391864929 Henry Cohn, 2025, needs more optimization.
6 1008 0.837393643211 Henry Cohn, 2026, needs more optimization.
6 1009 0.837522537170 Henry Cohn, 2025, needs more optimization.
6 1010 0.837636537050 Henry Cohn, 2025, needs more optimization.
6 1012 0.837675282618 Henry Cohn, 2026, needs more optimization.
6 1013 0.837809183769 Henry Cohn, 2025, needs more optimization.
6 1014 0.837809886773 Henry Cohn, 2026, needs more optimization.
6 1015 0.837940910005 Henry Cohn, 2025, needs more optimization.
6 1016 0.837946894777 Henry Cohn, 2025, needs more optimization.
6 1017 0.837962553501 Henry Cohn, 2026, needs more optimization.
6 1018 0.838155652623 Henry Cohn, 2026, needs more optimization.
6 1019 0.838161452587 Henry Cohn, 2025, needs more optimization.
6 1020 0.838339854919 Henry Cohn, 2025, needs more optimization.
6 1021 0.838343021300 Henry Cohn, 2026, needs more optimization.
6 1022 0.838428949157 Henry Cohn, 2026, needs more optimization.
6 1023 0.838513425608 Henry Cohn, 2025, needs more optimization.
6 1024 0.838621267399 Henry Cohn, 2026, needs more optimization.
7 15 0.098701776273 P. G. Adams, A numerical approach to Tamme's problem in Euclidean n-space, Master of Science thesis, Oregon State University, 1997, https://hdl.handle.net/1957/33911.
175⁢x3−49⁢x2−7⁢x+1
7 16 0.113320879601 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
Minimal polynomial listed in plain text data
7 17 0.124841583816 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
7 18 0.126131983623 P. G. Adams, A numerical approach to Tamme's problem in Euclidean n-space, Master of Science thesis, Oregon State University, 1997, https://hdl.handle.net/1957/33911.
47⁢x2+2⁢x−1
7 19 0.156597385418 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
1280⁢x6−352⁢x4−48⁢x3+37⁢x2+3⁢x−1
7 20 0.169520847199 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
23⁢x2+2⁢x−1
7 21 0.181523960801 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
7 22 0.182743997632 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
19⁢x2+2⁢x−1
7 23 0.182743997632 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
19⁢x2+2⁢x−1
7 24 0.182743997632 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
19⁢x2+2⁢x−1
7 25 0.214737233855 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
31⁢x2−2⁢x−1
7 26 0.231331430372 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
7 27 0.240549382010 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7 28 0.247356651208 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7 29 0.248893779344 H. Cohn, Small spherical and projective codes, data set, updated 2025, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7 30 0.249468282003 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7 31 0.254502767515 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7 32 0.265595699432 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7 33 0.270023386002 Henry Cohn, 2024.
7 34 0.277696496789 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
7 35 0.289773019868 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
7 36 0.299959896814 Henry Cohn, 2023.
7 37 0.310451288111 Henry Cohn, 2026.
7 39 0.316279494687 Henry Cohn, 2023.
71⁢x2+6⁢x−9
7 40 0.323843153340 Henry Cohn, 2023.
7 41 0.325408592469 Henry Cohn, 2023.
32⁢x4+40⁢x3−23⁢x2−4⁢x+2
7 42 0.329083455200 Henry Cohn, 2025.
7 43 0.329665776133 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
7 44 0.332131779753 Henry Cohn, 2025.
Minimal polynomial listed in plain text data
7 45 0.333226297127 Henry Cohn, 2026.
7 46 0.333312302687 Henry Cohn, 2025.
7 47 0.333332883018 Henry Cohn, 2026.
7 56* 0.333333333334 T. Gosset, On the regular and semi-regular figures in space of n dimensions, Messenger Math. 29 (1900), 43–48; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
3⁢x−1
7 57 0.389612708410 Henry Cohn, 2025.
7 58 0.393749423280 Henry Cohn, 2023.
7 59 0.403217495108 Henry Cohn, 2025.
7 60 0.407983464085 Henry Cohn, 2025.
7 61 0.412356098716 Henry Cohn, 2024.
7 62 0.414766349117 Henry Cohn, 2025.
7 63 0.415390831033 Henry Cohn, 2025.
7 64 0.420197073744 Henry Cohn, 2025.
7 67 0.421258543571 Henry Cohn, 2024.
622⁢x3−771⁢x2+288⁢x−31
7 68 0.428235713853 Henry Cohn, 2025.
7 69 0.428531302684 Henry Cohn, 2026.
7 70 0.428552368060 Henry Cohn, 2026.
7 78 0.428571428572 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
7⁢x−3
7 79 0.453278412444 Henry Cohn, 2024.
7 80 0.453887992064 Henry Cohn, 2024.
7 81 0.459667826759 Henry Cohn, 2025.
7 82 0.461219223470 Henry Cohn, 2025.
7 83 0.461669205843 Henry Cohn, 2024.
7 84 0.465073032663 Henry Cohn, 2025.
7 86 0.466580867327 Henry Cohn, 2025, needs more optimization.
7 87 0.469578821552 Henry Cohn, 2024.
7 88 0.473067267884 Henry Cohn, 2024.
7 89 0.474988257844 Henry Cohn, 2024.
7 90 0.475294477919 Henry Cohn, 2024.
7 91 0.479167604557 Henry Cohn, 2026.
7 92 0.480306853225 Henry Cohn, 2025.
7 93 0.482408792669 Henry Cohn, 2026.
7 94 0.483507258083 Henry Cohn, 2025.
7 96 0.486808303779 Henry Cohn, 2025.
7 97 0.487296284314 Henry Cohn, 2025.
7 98 0.489141129031 Henry Cohn, 2026.
7 99 0.494790287384 Henry Cohn, 2026, needs more optimization.
7 101 0.496533689719 Henry Cohn, 2026, needs more optimization.
7 102 0.496928744650 Henry Cohn, 2026, needs more optimization.
7 103 0.498541050865 Henry Cohn, 2026, needs more optimization.
7 106 0.499144603452 Henry Cohn, 2026, needs more optimization.
7 107 0.499592044297 Henry Cohn, 2026, needs more optimization.
7 108 0.499944082669 Henry Cohn, 2026, needs more optimization.
7 109 0.499990542788 Henry Cohn, 2026, needs more optimization.
7 110 0.499999099965 Henry Cohn, 2026, needs more optimization.
7 111 0.499999997332 Henry Cohn, 2026, needs more optimization.
7 112 0.499999997662 Henry Cohn, 2026, needs more optimization.
7 126 0.5 A. Korkine and G. Zolotareff, Sur les formes quadratiques, Math. Ann. 6 (1873), 366–389, doi:10.1007/BF01442795; J. Leech, Six and seven dimensional non-lattice sphere packings, Canad. Math. Bull. 12 (1969), 151–155, doi:10.4153/CMB-1969-014-1; J. H. Conway and N. J. A. Sloane, What are all the best sphere packings in low dimensions?, Discrete Comput. Geom. 13 (1995), 383–403, doi:10.1007/BF02574051; H. Cohn, Y. Jiao, A. Kumar, and S. Torquato, Rigidity of spherical codes, Geom. Topol. 15 (2011), 2235–2273, doi:10.2140/gt.2011.15.2235, arXiv:1102.5060.
2⁢x−1
7 127 0.509963471599 Henry Cohn, 2025.
7 128 0.513867786048 Henry Cohn, 2026, needs more optimization.
7 129 0.518845743940 Henry Cohn, 2026, needs more optimization.
7 132 0.519151939817 Henry Cohn, 2026, needs more optimization.
7 134 0.519151940547 Henry Cohn, 2026, needs more optimization.
7 136 0.519153914325 Henry Cohn, 2026, needs more optimization.
7 137 0.519751518195 Henry Cohn, 2024.
7 138 0.527218738805 Henry Cohn, 2025.
7 141 0.531596764994 Henry Cohn, 2026, needs more optimization.
7 142 0.531667393940 Henry Cohn, 2025, needs more optimization.
7 144 0.531670507818 Henry Cohn, 2026, needs more optimization.
7 145 0.532801092831 Henry Cohn, 2026, needs more optimization.
7 146 0.532883690322 Henry Cohn, 2025.
7 147 0.533479772596 Henry Cohn, 2024.
7 148 0.533995828316 Henry Cohn, 2026.
7 149 0.546228057898 Henry Cohn, 2026, needs more optimization.
7 150 0.546228537761 Henry Cohn, 2026, needs more optimization.
7 151 0.546228627740 Henry Cohn, 2026, needs more optimization.
7 152 0.546229237935 Henry Cohn, 2026, needs more optimization.
7 153 0.546281099580 Henry Cohn, 2026, needs more optimization.
7 154 0.546281370439 Henry Cohn, 2026, needs more optimization.
7 155 0.548973616291 Henry Cohn, 2026, needs more optimization.
7 156 0.552241692045 Henry Cohn, 2026, needs more optimization.
7 157 0.557025332397 Henry Cohn, 2026, needs more optimization.
7 158 0.559633838899 Henry Cohn, 2026, needs more optimization.
7 161 0.560466667804 Henry Cohn, 2026, needs more optimization.
7 162 0.561765794056 Henry Cohn, 2026, needs more optimization.
7 163 0.561767689319 Henry Cohn, 2026, needs more optimization.
7 168 0.563371438124 Henry Cohn, 2026, needs more optimization.
7 169 0.563588109639 Henry Cohn, 2026, needs more optimization.
7 170 0.563592107095 Henry Cohn, 2026, needs more optimization.
7 171 0.569095738763 Henry Cohn, 2026, needs more optimization.
7 173 0.570443896022 Henry Cohn, 2026, needs more optimization.
7 176 0.570443896023 Henry Cohn, 2026, needs more optimization.
7 177 0.570454519900 Henry Cohn, 2026, needs more optimization.
7 178 0.570455862607 Henry Cohn, 2026, needs more optimization.
7 180 0.570549323515 Henry Cohn, 2026, needs more optimization.
7 181 0.573146880911 Henry Cohn, 2025, needs more optimization.
7 182 0.577350269190 J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment. Math. 5 (1996), 139–159, https://projecteuclid.org/euclid.em/1047565645; B. Ballinger, G. Blekherman, H. Cohn, N. Giansiracusa, E. Kelly, and A. Schürmann, Experimental study of energy-minimizing point configurations on spheres, Experiment. Math. 18 (2009), 257–283, https://projecteuclid.org/euclid.em/1259158465.
3⁢x2−1
7 183 0.587541965804 Ilmari Vahteristo, 2026.
7 184 0.590392362228 Henry Cohn, 2026, needs more optimization.
7 185 0.592031258395 Henry Cohn, 2024, needs more optimization.
7 186 0.592610444725 Henry Cohn, 2026, needs more optimization.
7 188 0.593606290207 Henry Cohn, 2026, needs more optimization.
7 189 0.594291958748 Henry Cohn, 2026, needs more optimization.
7 191 0.594819649517 Henry Cohn, 2026, needs more optimization.
7 192 0.596061486654 Henry Cohn, 2026, needs more optimization.
7 193 0.596071968555 Henry Cohn, 2026, needs more optimization.
7 194 0.599360499965 Henry Cohn, 2024, needs more optimization.
7 195 0.601540224587 Henry Cohn, 2024, needs more optimization.
7 196 0.601793608585 Henry Cohn, 2024, needs more optimization.
7 197 0.603597835671 Henry Cohn, 2026, needs more optimization.
7 198 0.604006403946 Henry Cohn, 2025.
7 199 0.605261083349 Henry Cohn, 2024, needs more optimization.
7 200 0.605866105540 Henry Cohn, 2024, needs more optimization.
7 201 0.606555716151 Henry Cohn, 2026, needs more optimization.
7 202 0.607791427450 Henry Cohn, 2026, needs more optimization.
7 203 0.608285548010 Henry Cohn, 2026, needs more optimization.
7 204 0.609154796631 Henry Cohn, 2026, needs more optimization.
7 205 0.611021004540 Henry Cohn, 2026, needs more optimization.
7 206 0.611945534082 Henry Cohn, 2024, needs more optimization.
7 207 0.612727397745 Henry Cohn, 2024, needs more optimization.
7 208 0.613448534998 Henry Cohn, 2024, needs more optimization.
7 209 0.614590794819 Henry Cohn, 2024, needs more optimization.
7 210 0.614894346303 Henry Cohn, 2024, needs more optimization.
7 211 0.616021679004 Henry Cohn, 2024, needs more optimization.
7 212 0.616329554386 Henry Cohn, 2026, needs more optimization.
7 213 0.617073701156 Henry Cohn, 2024, needs more optimization.
7 214 0.617833350687 Henry Cohn, 2026, needs more optimization.
7 215 0.618739761564 Henry Cohn, 2026, needs more optimization.
7 216 0.619599983206 Henry Cohn, 2024, needs more optimization.
7 217 0.620540826883 Henry Cohn, 2026, needs more optimization.
7 218 0.621368072363 Henry Cohn, 2024, needs more optimization.
7 219 0.621900185806 Henry Cohn, 2026, needs more optimization.
7 220 0.622604993923 Henry Cohn, 2024, needs more optimization.
7 221 0.624023095035 Henry Cohn, 2024, needs more optimization.
7 222 0.624410753011 Henry Cohn, 2026, needs more optimization.
7 223 0.624822505678 Henry Cohn, 2026, needs more optimization.
7 224 0.625206654600 Henry Cohn, 2026, needs more optimization.
7 225 0.625872966956 Henry Cohn, 2024, needs more optimization.
7 226 0.627180587577 Henry Cohn, 2026, needs more optimization.
7 227 0.627364742643 Henry Cohn, 2026, needs more optimization.
7 228 0.628144528595 Henry Cohn, 2026, needs more optimization.
7 229 0.629183026831 Henry Cohn, 2026, needs more optimization.
7 230 0.630264678870 Henry Cohn, 2024, needs more optimization.
7 231 0.630549078404 Henry Cohn, 2024, needs more optimization.
7 232 0.631248222170 Henry Cohn, 2024, needs more optimization.
7 233 0.631901836958 Henry Cohn, 2024, needs more optimization.
7 234 0.632643043718 Henry Cohn, 2024, needs more optimization.
7 235 0.633043566268 Henry Cohn, 2026, needs more optimization.
7 236 0.633943127321 Henry Cohn, 2024, needs more optimization.
7 237 0.634261704526 Henry Cohn, 2026, needs more optimization.
7 238 0.634781311206 Henry Cohn, 2024, needs more optimization.
7 239 0.635356766795 Henry Cohn, 2024, needs more optimization.
7 240 0.635677240819 Henry Cohn, 2024, needs more optimization.
7 241 0.636614389125 Henry Cohn, 2024, needs more optimization.
7 242 0.636965575506 Henry Cohn, 2024, needs more optimization.
7 243 0.637513507990 Henry Cohn, 2024, needs more optimization.
7 244 0.638074677610 Henry Cohn, 2024, needs more optimization.
7 245 0.638592844169 Henry Cohn, 2025, needs more optimization.
7 246 0.638771563838 Henry Cohn, 2025, needs more optimization.
7 247 0.639347723126 Henry Cohn, 2025, needs more optimization.
7 248 0.640032835036 Henry Cohn, 2024, needs more optimization.
7 249 0.640408857728 Henry Cohn, 2025, needs more optimization.
7 250 0.640982436344 Henry Cohn, 2025, needs more optimization.
7 251 0.641158392745 Henry Cohn, 2026, needs more optimization.
7 252 0.641653401103 Henry Cohn, 2026, needs more optimization.
7 253 0.641879425965 Henry Cohn, 2025, needs more optimization.
7 254 0.642941709635 Henry Cohn, 2026, needs more optimization.
7 255 0.643269607048 Henry Cohn, 2025, needs more optimization.
7 256 0.643614466517 Henry Cohn, 2025, needs more optimization.
7 257 0.644347933308 Henry Cohn, 2026, needs more optimization.
7 258 0.644908976495 Henry Cohn, 2026, needs more optimization.
7 259 0.645222821952 Henry Cohn, 2026, needs more optimization.
7 260 0.645645320007 Henry Cohn, 2026, needs more optimization.
7 261 0.645847145637 Henry Cohn, 2026, needs more optimization.
7 262 0.646146152305 Henry Cohn, 2026, needs more optimization.
7 263 0.647124066463 Henry Cohn, 2026, needs more optimization.
7 264 0.647393555376 Henry Cohn, 2026, needs more optimization.
7 265 0.648281926512 Henry Cohn, 2026, needs more optimization.
7 266 0.648454561163 Henry Cohn, 2026, needs more optimization.
7 267 0.648884959686 Henry Cohn, 2026, needs more optimization.
7 268 0.649484032054 Henry Cohn, 2025, needs more optimization.
7 269 0.649637461961 Henry Cohn, 2026, needs more optimization.
7 270 0.650037311217 Henry Cohn, 2026, needs more optimization.
7 271 0.650210530176 Henry Cohn, 2026, needs more optimization.
7 272 0.650872965179 Henry Cohn, 2025, needs more optimization.
7 273 0.651436196216 Henry Cohn, 2026, needs more optimization.
7 274 0.651535200058 Henry Cohn, 2026, needs more optimization.
7 275 0.651758524713 Henry Cohn, 2026, needs more optimization.
7 276 0.652816200390 Henry Cohn, 2025, needs more optimization.
7 277 0.652937956970 Henry Cohn, 2026, needs more optimization.
7 278 0.653567114525 Henry Cohn, 2026, needs more optimization.
7 279 0.654130199784 Henry Cohn, 2026, needs more optimization.
7 280 0.654181712325 Henry Cohn, 2026, needs more optimization.
7 281 0.654947513766 Henry Cohn, 2026, needs more optimization.
7 282 0.655071481483 Henry Cohn, 2025, needs more optimization.
7 283 0.655694421143 Henry Cohn, 2026, needs more optimization.
7 284 0.655939395423 Henry Cohn, 2026, needs more optimization.
7 285 0.656544346448 Henry Cohn, 2026, needs more optimization.
7 286 0.657024138855 Henry Cohn, 2026, needs more optimization.
7 287 0.657332541225 Henry Cohn, 2026, needs more optimization.
7 288 0.657574191509 Henry Cohn, 2026, needs more optimization.
7 289 0.658060848385 Henry Cohn, 2026, needs more optimization.
7 290 0.658671892385 Henry Cohn, 2026, needs more optimization.
7 291 0.659127213481 Henry Cohn, 2026, needs more optimization.
7 292 0.659401922113 Henry Cohn, 2026, needs more optimization.
7 293 0.659727765304 Henry Cohn, 2026, needs more optimization.
7 294 0.660045005661 Henry Cohn, 2026, needs more optimization.
7 295 0.661026050450 Henry Cohn, 2026, needs more optimization.
7 296 0.661083622910 Henry Cohn, 2026, needs more optimization.
7 297 0.661248245899 Henry Cohn, 2025, needs more optimization.
7 298 0.661780957395 Henry Cohn, 2026, needs more optimization.
7 299 0.662450024429 Henry Cohn, 2026, needs more optimization.
7 300 0.662682038294 Henry Cohn, 2026, needs more optimization.
7 301 0.663480479645 Henry Cohn, 2025, needs more optimization.
7 302 0.663759454150 Henry Cohn, 2025, needs more optimization.
7 303 0.663998669282 Henry Cohn, 2026, needs more optimization.
7 304 0.664599851270 Henry Cohn, 2026, needs more optimization.
7 305 0.664628042274 Henry Cohn, 2025, needs more optimization.
7 306 0.664738733263 Henry Cohn, 2026, needs more optimization.
7 307 0.665702963255 Henry Cohn, 2025, needs more optimization.
7 308 0.666037244322 Henry Cohn, 2025, needs more optimization.
7 358 0.666666666667 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−2
7 359 0.675386736306 Henry Cohn, 2026, needs more optimization.
7 360 0.675672261492 Henry Cohn, 2026, needs more optimization.
7 361 0.675712378451 Henry Cohn, 2026, needs more optimization.
7 362 0.675811135637 Henry Cohn, 2026, needs more optimization.
7 363 0.675811653557 Henry Cohn, 2026, needs more optimization.
7 364 0.675854054558 Henry Cohn, 2026, needs more optimization.
7 365 0.675946641714 Henry Cohn, 2026, needs more optimization.
7 366 0.676117098486 Henry Cohn, 2026, needs more optimization.
7 367 0.676399959676 Henry Cohn, 2026, needs more optimization.
7 368 0.676415352949 Henry Cohn, 2026, needs more optimization.
7 369 0.676479305561 Henry Cohn, 2026, needs more optimization.
7 372 0.676737424673 Henry Cohn, 2026, needs more optimization.
7 373 0.676833567738 Henry Cohn, 2026, needs more optimization.
7 376 0.677059596678 Henry Cohn, 2026, needs more optimization.
7 380 0.677085973391 Henry Cohn, 2026, needs more optimization.
7 381 0.677446098721 Henry Cohn, 2026, needs more optimization.
7 382 0.677466298004 Henry Cohn, 2026, needs more optimization.
7 383 0.678022967422 Henry Cohn, 2026, needs more optimization.
7 384 0.679172662319 Henry Cohn, 2026, needs more optimization.
7 385 0.679178805122 Henry Cohn, 2026, needs more optimization.
7 386 0.679753598396 Henry Cohn, 2026, needs more optimization.
7 388 0.680312167273 Henry Cohn, 2026, needs more optimization.
7 389 0.680994589993 Henry Cohn, 2026, needs more optimization.
7 390 0.681057709175 Henry Cohn, 2026, needs more optimization.
7 391 0.681263351807 Henry Cohn, 2026, needs more optimization.
7 392 0.681696095783 Henry Cohn, 2026, needs more optimization.
7 394 0.681765586423 Henry Cohn, 2026, needs more optimization.
7 395 0.681798498173 Henry Cohn, 2026, needs more optimization.
7 396 0.682955969683 Henry Cohn, 2026, needs more optimization.
7 397 0.682997247619 Henry Cohn, 2026, needs more optimization.
7 398 0.683036748947 Henry Cohn, 2026, needs more optimization.
7 399 0.683110520018 Henry Cohn, 2026, needs more optimization.
7 400 0.683129736371 Henry Cohn, 2026, needs more optimization.
7 401 0.683185948128 Henry Cohn, 2026, needs more optimization.
7 402 0.683291958276 Henry Cohn, 2026, needs more optimization.
7 403 0.683318714028 Henry Cohn, 2026, needs more optimization.
7 404 0.683320042580 Henry Cohn, 2026, needs more optimization.
7 405 0.683357014411 Henry Cohn, 2026, needs more optimization.
7 406 0.690932444651 Henry Cohn, 2025, needs more optimization.
7 407 0.691685829843 Henry Cohn, 2026, needs more optimization.
7 408 0.692257645580 Henry Cohn, 2026, needs more optimization.
7 409 0.692332039010 Henry Cohn, 2025, needs more optimization.
7 410 0.692414746541 Henry Cohn, 2025, needs more optimization.
7 411 0.692787928477 Henry Cohn, 2025, needs more optimization.
7 412 0.692958018599 Henry Cohn, 2026, needs more optimization.
7 413 0.693125695547 Henry Cohn, 2025, needs more optimization.
7 414 0.693154749248 Henry Cohn, 2025, needs more optimization.
7 415 0.693162668354 Henry Cohn, 2025, needs more optimization.
7 416 0.694123742176 Henry Cohn, 2025, needs more optimization.
7 417 0.694287009188 Henry Cohn, 2025, needs more optimization.
7 418 0.694523585349 Henry Cohn, 2025, needs more optimization.
7 419 0.694815792826 Henry Cohn, 2026, needs more optimization.
7 420 0.695128563933 Henry Cohn, 2025, needs more optimization.
7 421 0.695130508518 Henry Cohn, 2025, needs more optimization.
7 422 0.695176221166 Henry Cohn, 2025, needs more optimization.
7 423 0.695830132382 Henry Cohn, 2025, needs more optimization.
7 424 0.695880985033 Henry Cohn, 2025, needs more optimization.
7 425 0.696154846704 Henry Cohn, 2025, needs more optimization.
7 426 0.696220870137 Henry Cohn, 2025, needs more optimization.
7 427 0.696335833512 Henry Cohn, 2025, needs more optimization.
7 428 0.696904394283 Henry Cohn, 2026, needs more optimization.
7 429 0.696957305399 Henry Cohn, 2025, needs more optimization.
7 430 0.697024460578 Henry Cohn, 2025, needs more optimization.
7 431 0.697198226158 Henry Cohn, 2025, needs more optimization.
7 432 0.697758355591 Henry Cohn, 2025, needs more optimization.
7 434 0.698064930275 Henry Cohn, 2026, needs more optimization.
7 436 0.698129161773 Henry Cohn, 2025, needs more optimization.
7 438 0.698768530471 Henry Cohn, 2025, needs more optimization.
7 439 0.699057471161 Henry Cohn, 2025, needs more optimization.
7 440 0.699564497374 Henry Cohn, 2025, needs more optimization.
7 441 0.699943203361 Henry Cohn, 2026, needs more optimization.
7 442 0.700293285076 Henry Cohn, 2025, needs more optimization.
7 444 0.700938073780 Henry Cohn, 2025, needs more optimization.
7 445 0.700946567027 Henry Cohn, 2025, needs more optimization.
7 446 0.700962130467 Henry Cohn, 2025, needs more optimization.
7 447 0.701190449341 Henry Cohn, 2025, needs more optimization.
7 448 0.701776571024 Henry Cohn, 2025, needs more optimization.
7 449 0.702022842893 Henry Cohn, 2025, needs more optimization.
7 450 0.702810548686 Henry Cohn, 2025, needs more optimization.
7 451 0.702836794920 Henry Cohn, 2026, needs more optimization.
7 452 0.703104019437 Henry Cohn, 2026, needs more optimization.
7 453 0.703553853189 Henry Cohn, 2025, needs more optimization.
7 454 0.703590992781 Henry Cohn, 2025, needs more optimization.
7 455 0.703646141098 Henry Cohn, 2025, needs more optimization.
7 458 0.704114722772 Henry Cohn, 2025, needs more optimization.
7 459 0.704603392874 Henry Cohn, 2025, needs more optimization.
7 460 0.704691314146 Henry Cohn, 2026, needs more optimization.
7 461 0.705051861668 Henry Cohn, 2026, needs more optimization.
7 462 0.705056506687 Henry Cohn, 2025, needs more optimization.
7 463 0.705379494979 Henry Cohn, 2025, needs more optimization.
7 464 0.705388063719 Henry Cohn, 2025, needs more optimization.
7 465 0.705399208446 Henry Cohn, 2025, needs more optimization.
7 466 0.705439358343 Henry Cohn, 2026, needs more optimization.
7 467 0.705764381751 Henry Cohn, 2025, needs more optimization.
7 468 0.705859692358 Henry Cohn, 2025, needs more optimization.
7 469 0.705879757078 Henry Cohn, 2025, needs more optimization.
7 472 0.706158356996 Henry Cohn, 2025, needs more optimization.
7 473 0.706329190915 Henry Cohn, 2025, needs more optimization.
7 474 0.706718336008 Henry Cohn, 2025, needs more optimization.
7 475 0.707007270167 Henry Cohn, 2025, needs more optimization.
7 476 0.707415911476 Henry Cohn, 2025, needs more optimization.
7 477 0.707552845511 Henry Cohn, 2025, needs more optimization.
7 478 0.707831690404 Henry Cohn, 2026, needs more optimization.
7 479 0.708089164268 Henry Cohn, 2026, needs more optimization.
7 480 0.708092903508 Henry Cohn, 2026, needs more optimization.
7 481 0.708095396023 Henry Cohn, 2025, needs more optimization.
7 482 0.708101389020 Henry Cohn, 2025, needs more optimization.
7 484 0.708113876563 Henry Cohn, 2026, needs more optimization.
7 486 0.708180044040 Henry Cohn, 2026, needs more optimization.
7 488 0.708460763259 Henry Cohn, 2026, needs more optimization.
7 489 0.708483139185 Henry Cohn, 2026, needs more optimization.
7 490 0.708554397780 Henry Cohn, 2026, needs more optimization.
7 491 0.708679022412 Henry Cohn, 2026, needs more optimization.
7 492 0.708950875015 Henry Cohn, 2026, needs more optimization.
7 493 0.709329693366 Henry Cohn, 2026, needs more optimization.
7 495 0.709342566356 Henry Cohn, 2026, needs more optimization.
7 497 0.709385652205 Henry Cohn, 2026, needs more optimization.
7 498 0.710177029821 Henry Cohn, 2026, needs more optimization.
7 500 0.710662666537 Henry Cohn, 2026, needs more optimization.
7 501 0.710715390615 Henry Cohn, 2026, needs more optimization.
7 502 0.710741250118 Henry Cohn, 2026, needs more optimization.
7 503 0.710804090259 Henry Cohn, 2026, needs more optimization.
7 504 0.711088772535 Henry Cohn, 2026, needs more optimization.
7 505 0.711110226360 Henry Cohn, 2026, needs more optimization.
7 506 0.711127506791 Henry Cohn, 2026, needs more optimization.
7 508 0.711500454141 Henry Cohn, 2026, needs more optimization.
7 510 0.711574159107 Henry Cohn, 2026, needs more optimization.
7 512 0.712280029239 Henry Cohn, 2026, needs more optimization.
7 513 0.712509660408 Henry Cohn, 2026, needs more optimization.
7 514 0.712574202709 Henry Cohn, 2026, needs more optimization.
7 516 0.713742845397 Henry Cohn, 2026, needs more optimization.
7 520 0.713756365533 Henry Cohn, 2026, needs more optimization.
7 632 0.714285714286 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−5
7 633 0.738212208737 Henry Cohn, 2025, needs more optimization.
7 634 0.738290846780 Henry Cohn, 2025, needs more optimization.
7 635 0.738514957398 Henry Cohn, 2025, needs more optimization.
7 636 0.738698883856 Henry Cohn, 2026, needs more optimization.
7 637 0.738806782327 Henry Cohn, 2026, needs more optimization.
7 638 0.738808878795 Henry Cohn, 2026, needs more optimization.
7 639 0.739206238069 Henry Cohn, 2026, needs more optimization.
7 640 0.739410094536 Henry Cohn, 2026, needs more optimization.
7 641 0.739502099602 Henry Cohn, 2026, needs more optimization.
7 642 0.739557467245 Henry Cohn, 2025, needs more optimization.
7 643 0.739677329979 Henry Cohn, 2025, needs more optimization.
7 644 0.739935385449 Henry Cohn, 2025, needs more optimization.
7 645 0.740062240505 Henry Cohn, 2026, needs more optimization.
7 647 0.740092985796 Henry Cohn, 2025, needs more optimization.
7 648 0.740196705783 Henry Cohn, 2025, needs more optimization.
7 649 0.740485861272 Henry Cohn, 2025, needs more optimization.
7 650 0.740489698240 Henry Cohn, 2025, needs more optimization.
7 651 0.740776270368 Henry Cohn, 2025, needs more optimization.
7 652 0.740795119630 Henry Cohn, 2025, needs more optimization.
7 653 0.740853998009 Henry Cohn, 2025, needs more optimization.
7 654 0.741007859949 Henry Cohn, 2025, needs more optimization.
7 655 0.741108984239 Henry Cohn, 2025, needs more optimization.
7 656 0.741266212351 Henry Cohn, 2025, needs more optimization.
7 657 0.741423963467 Henry Cohn, 2026, needs more optimization.
7 658 0.741587488811 Henry Cohn, 2026, needs more optimization.
7 659 0.741791365530 Henry Cohn, 2025, needs more optimization.
7 660 0.741797653020 Henry Cohn, 2025, needs more optimization.
7 661 0.742249283144 Henry Cohn, 2025, needs more optimization.
7 662 0.742253219354 Henry Cohn, 2025, needs more optimization.
7 663 0.742720226175 Henry Cohn, 2025, needs more optimization.
7 664 0.742758591108 Henry Cohn, 2025, needs more optimization.
7 665 0.742766297023 Henry Cohn, 2025, needs more optimization.
7 666 0.742808097093 Henry Cohn, 2026, needs more optimization.
7 667 0.743019244916 Henry Cohn, 2025, needs more optimization.
7 668 0.743123047682 Henry Cohn, 2026, needs more optimization.
7 669 0.743288678978 Henry Cohn, 2026, needs more optimization.
7 670 0.743468933950 Henry Cohn, 2025, needs more optimization.
7 671 0.743614433987 Henry Cohn, 2025, needs more optimization.
7 672 0.743762300778 Henry Cohn, 2026, needs more optimization.
7 673 0.743822788935 Henry Cohn, 2025, needs more optimization.
7 674 0.744018818012 Henry Cohn, 2025, needs more optimization.
7 675 0.744115543873 Henry Cohn, 2025, needs more optimization.
7 676 0.744122647767 Henry Cohn, 2025, needs more optimization.
7 677 0.744214110035 Henry Cohn, 2025, needs more optimization.
7 678 0.744328612114 Henry Cohn, 2025, needs more optimization.
7 679 0.744583672177 Henry Cohn, 2026, needs more optimization.
7 680 0.744712905884 Henry Cohn, 2026, needs more optimization.
7 682 0.745009803213 Henry Cohn, 2025, needs more optimization.
7 683 0.745055262785 Henry Cohn, 2025, needs more optimization.
7 684 0.745058045885 Henry Cohn, 2026, needs more optimization.
7 685 0.745265338477 Henry Cohn, 2025, needs more optimization.
7 686 0.745379029546 Henry Cohn, 2026, needs more optimization.
7 687 0.745383341663 Henry Cohn, 2025, needs more optimization.
7 688 0.745567673171 Henry Cohn, 2025, needs more optimization.
7 689 0.745734483386 Henry Cohn, 2025, needs more optimization.
7 690 0.746062644359 Henry Cohn, 2025, needs more optimization.
7 691 0.746134729202 Henry Cohn, 2025, needs more optimization.
7 692 0.746182295167 Henry Cohn, 2025, needs more optimization.
7 693 0.746191941399 Henry Cohn, 2025, needs more optimization.
7 694 0.746428038640 Henry Cohn, 2026, needs more optimization.
7 695 0.746453416511 Henry Cohn, 2025, needs more optimization.
7 696 0.746467272171 Henry Cohn, 2025, needs more optimization.
7 697 0.746714567018 Henry Cohn, 2025, needs more optimization.
7 698 0.746721146572 Henry Cohn, 2025, needs more optimization.
7 699 0.746954039717 Henry Cohn, 2025, needs more optimization.
7 700 0.747005610616 Henry Cohn, 2026, needs more optimization.
7 701 0.747371942318 Henry Cohn, 2025, needs more optimization.
7 702 0.747505256810 Henry Cohn, 2026, needs more optimization.
7 703 0.747608060458 Henry Cohn, 2026, needs more optimization.
7 704 0.747814725681 Henry Cohn, 2026, needs more optimization.
7 705 0.747824940385 Henry Cohn, 2025, needs more optimization.
7 706 0.748150243104 Henry Cohn, 2025, needs more optimization.
7 707 0.748167879463 Henry Cohn, 2025, needs more optimization.
7 708 0.748223892857 Henry Cohn, 2026, needs more optimization.
7 709 0.748384853776 Henry Cohn, 2025, needs more optimization.
7 710 0.748424009839 Henry Cohn, 2026, needs more optimization.
7 711 0.748678551785 Henry Cohn, 2026, needs more optimization.
7 712 0.748806097949 Henry Cohn, 2026, needs more optimization.
7 713 0.748972920661 Henry Cohn, 2026, needs more optimization.
7 714 0.749018670235 Henry Cohn, 2025, needs more optimization.
7 715 0.749221951020 Henry Cohn, 2025, needs more optimization.
7 716 0.749387656241 Henry Cohn, 2026, needs more optimization.
7 882 0.75 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
4⁢x−3
7 883 0.766304091493 Henry Cohn, 2025, needs more optimization.
7 884 0.766418771944 Henry Cohn, 2025, needs more optimization.
7 885 0.766525239704 Henry Cohn, 2025, needs more optimization.
7 886 0.766527594674 Henry Cohn, 2025, needs more optimization.
7 887 0.766864400562 Henry Cohn, 2026, needs more optimization.
7 888 0.766885779552 Henry Cohn, 2026, needs more optimization.
7 889 0.766889331520 Henry Cohn, 2026, needs more optimization.
7 890 0.767018124487 Henry Cohn, 2025, needs more optimization.
7 891 0.767083852054 Henry Cohn, 2026, needs more optimization.
7 892 0.767231569550 Henry Cohn, 2025, needs more optimization.
7 893 0.767251169955 Henry Cohn, 2026, needs more optimization.
7 894 0.767257094381 Henry Cohn, 2026, needs more optimization.
7 895 0.767391546637 Henry Cohn, 2025, needs more optimization.
7 896 0.767401946186 Henry Cohn, 2025, needs more optimization.
7 897 0.767681720564 Henry Cohn, 2025, needs more optimization.
7 898 0.767731229371 Henry Cohn, 2026, needs more optimization.
7 899 0.767736873146 Henry Cohn, 2025, needs more optimization.
7 900 0.767809065227 Henry Cohn, 2026, needs more optimization.
7 901 0.768010151877 Henry Cohn, 2025, needs more optimization.
7 902 0.768013173488 Henry Cohn, 2025, needs more optimization.
7 904 0.768138005293 Henry Cohn, 2025, needs more optimization.
7 905 0.768349270409 Henry Cohn, 2025, needs more optimization.
7 906 0.768388903761 Henry Cohn, 2026, needs more optimization.
7 907 0.768518067748 Henry Cohn, 2025, needs more optimization.
7 908 0.768580271112 Henry Cohn, 2025, needs more optimization.
7 909 0.768713496939 Henry Cohn, 2025, needs more optimization.
7 910 0.768739341134 Henry Cohn, 2025, needs more optimization.
7 911 0.768770505285 Henry Cohn, 2026, needs more optimization.
7 913 0.768957366848 Henry Cohn, 2025, needs more optimization.
7 914 0.768959087661 Henry Cohn, 2026, needs more optimization.
7 915 0.769192254989 Henry Cohn, 2025, needs more optimization.
7 916 0.769195854871 Henry Cohn, 2026, needs more optimization.
7 917 0.769205025913 Henry Cohn, 2025, needs more optimization.
7 918 0.769532233218 Henry Cohn, 2025, needs more optimization.
7 919 0.769536044854 Henry Cohn, 2025, needs more optimization.
7 920 0.769700440865 Henry Cohn, 2025, needs more optimization.
7 921 0.769706804461 Henry Cohn, 2025, needs more optimization.
7 922 0.769879798173 Henry Cohn, 2026, needs more optimization.
7 923 0.769907148927 Henry Cohn, 2026, needs more optimization.
7 924 0.769923720137 Henry Cohn, 2026, needs more optimization.
7 925 0.769964729931 Henry Cohn, 2025, needs more optimization.
7 926 0.769997961235 Henry Cohn, 2025, needs more optimization.
7 927 0.770123058479 Henry Cohn, 2025, needs more optimization.
7 928 0.770256536122 Henry Cohn, 2026, needs more optimization.
7 929 0.770260744309 Henry Cohn, 2026, needs more optimization.
7 930 0.770302505224 Henry Cohn, 2025, needs more optimization.
7 931 0.770575709793 Henry Cohn, 2025, needs more optimization.
7 932 0.770579743316 Henry Cohn, 2025, needs more optimization.
7 933 0.770595690567 Henry Cohn, 2025, needs more optimization.
7 934 0.770626503767 Henry Cohn, 2026, needs more optimization.
7 935 0.770770168786 Henry Cohn, 2025, needs more optimization.
7 937 0.770899391053 Henry Cohn, 2026, needs more optimization.
7 938 0.771165856307 Henry Cohn, 2025, needs more optimization.
7 939 0.771169572134 Henry Cohn, 2025, needs more optimization.
7 940 0.771215436337 Henry Cohn, 2026, needs more optimization.
7 941 0.771239312708 Henry Cohn, 2025, needs more optimization.
7 943 0.771360024917 Henry Cohn, 2026, needs more optimization.
7 944 0.771503310438 Henry Cohn, 2025, needs more optimization.
7 945 0.771522679568 Henry Cohn, 2026, needs more optimization.
7 946 0.771742521096 Henry Cohn, 2025, needs more optimization.
7 948 0.771748841996 Henry Cohn, 2025, needs more optimization.
7 949 0.771757569216 Henry Cohn, 2025, needs more optimization.
7 950 0.771897005109 Henry Cohn, 2026, needs more optimization.
7 951 0.772123382659 Henry Cohn, 2025, needs more optimization.
7 952 0.772237080380 Henry Cohn, 2026, needs more optimization.
7 953 0.772239159993 Henry Cohn, 2026, needs more optimization.
7 954 0.772255181222 Henry Cohn, 2026, needs more optimization.
7 955 0.772542605323 Henry Cohn, 2025, needs more optimization.
7 956 0.772595320218 Henry Cohn, 2025, needs more optimization.
7 957 0.772601217064 Henry Cohn, 2026, needs more optimization.
7 959 0.772738527814 Henry Cohn, 2025, needs more optimization.
7 960 0.772837170696 Henry Cohn, 2026, needs more optimization.
7 961 0.772843474814 Henry Cohn, 2025, needs more optimization.
7 962 0.772920980658 Henry Cohn, 2026, needs more optimization.
7 963 0.773161630297 Henry Cohn, 2025, needs more optimization.
7 965 0.773200621725 Henry Cohn, 2025, needs more optimization.
7 966 0.773221993721 Henry Cohn, 2026, needs more optimization.
7 967 0.773310465530 Henry Cohn, 2026, needs more optimization.
7 968 0.773534895672 Henry Cohn, 2025, needs more optimization.
7 969 0.773634537960 Henry Cohn, 2025, needs more optimization.
7 970 0.773634633709 Henry Cohn, 2026, needs more optimization.
7 971 0.773822099300 Henry Cohn, 2025, needs more optimization.
7 972 0.773827494958 Henry Cohn, 2025, needs more optimization.
7 973 0.773834788495 Henry Cohn, 2025, needs more optimization.
7 974 0.773950544892 Henry Cohn, 2026, needs more optimization.
7 975 0.774070505394 Henry Cohn, 2026, needs more optimization.
7 976 0.774179541403 Henry Cohn, 2026, needs more optimization.
7 977 0.774221790291 Henry Cohn, 2025, needs more optimization.
7 978 0.774231409619 Henry Cohn, 2025, needs more optimization.
7 979 0.774443310796 Henry Cohn, 2025, needs more optimization.
7 980 0.774464634630 Henry Cohn, 2026, needs more optimization.
7 981 0.774489936361 Henry Cohn, 2025, needs more optimization.
7 982 0.774495818164 Henry Cohn, 2026, needs more optimization.
7 983 0.774644943776 Henry Cohn, 2026, needs more optimization.
7 985 0.774756465462 Henry Cohn, 2025, needs more optimization.
7 986 0.774774748227 Henry Cohn, 2025, needs more optimization.
7 987 0.774872741252 Henry Cohn, 2025, needs more optimization.
7 988 0.775041594845 Henry Cohn, 2025, needs more optimization.
7 989 0.775061512097 Henry Cohn, 2025, needs more optimization.
7 990 0.775268368778 Henry Cohn, 2025, needs more optimization.
7 991 0.775275612377 Henry Cohn, 2025, needs more optimization.
7 992 0.775423925764 Henry Cohn, 2025, needs more optimization.
7 993 0.775430697361 Henry Cohn, 2026, needs more optimization.
7 994 0.775449990401 Henry Cohn, 2026, needs more optimization.
7 995 0.775632598837 Henry Cohn, 2025, needs more optimization.
7 996 0.775669217867 Henry Cohn, 2026, needs more optimization.
7 997 0.775704293887 Henry Cohn, 2025, needs more optimization.
7 998 0.775770821979 Henry Cohn, 2026, needs more optimization.
7 999 0.775775463625 Henry Cohn, 2025, needs more optimization.
7 1000 0.775855223040 Henry Cohn, 2026, needs more optimization.
7 1001 0.776024150867 Henry Cohn, 2025, needs more optimization.
7 1002 0.776036634130 Henry Cohn, 2026, needs more optimization.
7 1003 0.776176572478 Henry Cohn, 2025, needs more optimization.
7 1004 0.776184751487 Henry Cohn, 2025, needs more optimization.
7 1005 0.776327111003 Henry Cohn, 2025, needs more optimization.
7 1006 0.776380105971 Henry Cohn, 2025, needs more optimization.
7 1007 0.776425871372 Henry Cohn, 2025, needs more optimization.
7 1008 0.776753227999 Henry Cohn, 2025, needs more optimization.
7 1009 0.776757501902 Henry Cohn, 2025, needs more optimization.
7 1010 0.776791148616 Henry Cohn, 2026, needs more optimization.
7 1012 0.776978114898 Henry Cohn, 2025, needs more optimization.
7 1013 0.777161042973 Henry Cohn, 2025, needs more optimization.
7 1014 0.777180183121 Henry Cohn, 2025, needs more optimization.
7 1015 0.777231130326 Henry Cohn, 2025, needs more optimization.
7 1016 0.777352916164 Henry Cohn, 2026, needs more optimization.
7 1017 0.777362033599 Henry Cohn, 2025, needs more optimization.
7 1018 0.777407561032 Henry Cohn, 2026, needs more optimization.
7 1019 0.777485256086 Henry Cohn, 2025, needs more optimization.
7 1020 0.777811702770 Henry Cohn, 2025, needs more optimization.
7 1021 0.777828074942 Henry Cohn, 2026, needs more optimization.
7 1022 0.777990478570 Henry Cohn, 2025, needs more optimization.
7 1023 0.777994305436 Henry Cohn, 2025, needs more optimization.
7 1024 0.778006655112 Henry Cohn, 2025, needs more optimization.
8 17 0.087733463324 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
288⁢x3−64⁢x2−8⁢x+1
8 18 0.099469572709 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
8 19 0.111409975027 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
Minimal polynomial listed in plain text data
8 20 0.119496866688 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
224⁢x3+60⁢x2−2⁢x−1
8 21 0.130601937482 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
28⁢x2+4⁢x−1
8 22 0.130601937482 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
28⁢x2+4⁢x−1
8 23 0.157169941990 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
Minimal polynomial listed in plain text data
8 24 0.157692144940 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
4⁢x4−4⁢x3−27⁢x2−2⁢x+1
8 25 0.164334174126 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
8 26 0.172652095036 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
8 27 0.179856457059 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
8 28 0.181158420022 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
36⁢x4+24⁢x3−36⁢x2+1
8 29 0.187922490077 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
8 30 0.203916279404 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
8 31 0.219706528517 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
8 32 0.227325452024 H. Cohn, Small spherical and projective codes, data set, updated 2023, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
95⁢x2−4⁢x−4
8 33 0.227325452024 Henry Cohn, 2023.
95⁢x2−4⁢x−4
8 34 0.233864616950 Henry Cohn, 2023.
26887680⁢x6+11003904⁢x5−444096⁢x4−594432⁢x3−55800⁢x2−480⁢x−1
8 35 0.236461100794 Henry Cohn, 2023.
4⁢x4+8⁢x3−20⁢x2+1
8 38 0.239920745566 Henry Cohn, 2023.
1088⁢x4−80⁢x2+1
8 39 0.243600150512 Henry Cohn, 2023.
1183744⁢x8+122880⁢x7−575488⁢x6−138240⁢x5+53632⁢x4+14976⁢x3−1568⁢x2−720⁢x+81
8 40 0.265121155593 Henry Cohn, 2025.
8 41 0.269588854450 Henry Cohn, 2025.
8 42 0.276791074187 Henry Cohn, 2023.
8 43 0.285155668748 Henry Cohn, 2025.
8 44 0.288883351523 Henry Cohn, 2026.
8 45 0.293504048474 Henry Cohn, 2025.
8 46 0.298271343353 Henry Cohn, 2025.
8 47 0.301070997037 Henry Cohn, 2025.
8 48 0.306796780995 Henry Cohn, 2025.
8 49 0.310558546149 Henry Cohn, 2025.
8 50 0.315283655377 Henry Cohn, 2025.
8 51 0.316850575857 Henry Cohn, 2023.
8 52 0.317147531407 Henry Cohn, 2025.
8 53 0.323010527708 Henry Cohn, 2025.
8 54 0.326002020004 Henry Cohn, 2025.
8 55 0.328647326389 Henry Cohn, 2025.
8 56 0.330635803908 Henry Cohn, 2024.
8 57 0.332158951387 Henry Cohn, 2025.
8 58 0.332676598414 Henry Cohn, 2025.
8 59 0.333047687244 Henry Cohn, 2025.
8 60 0.333177612425 Henry Cohn, 2025.
8 61 0.333249870325 Henry Cohn, 2025.
8 62 0.333256273907 Henry Cohn, 2025.
8 63 0.333327460019 Henry Cohn, 2025.
8 64 0.333333333334 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
3⁢x−1
8 65 0.340292894900 Henry Cohn, 2025.
8 66 0.348776902230 Henry Cohn, 2025.
8 67 0.350755730045 Henry Cohn, 2025.
8 68 0.352461904199 Henry Cohn, 2025.
8 71 0.353553390594 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
8⁢x2−1
8 72 0.357142857143 J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment. Math. 5 (1996), 139–159, https://projecteuclid.org/euclid.em/1047565645.
14⁢x−5
8 73 0.374360545517 Henry Cohn, 2023.
8 74 0.375030122030 Henry Cohn, 2025.
8 75 0.380147254829 Henry Cohn, 2024.
8 76 0.383280469013 Henry Cohn, 2023.
8 77 0.386305789989 Henry Cohn, 2025.
8 78 0.387879817423 Henry Cohn, 2025.
8 79 0.395049514668 Henry Cohn, 2024.
8 80 0.399272012697 Henry Cohn, 2024.
8 81 0.401670700481 Henry Cohn, 2026.
8 82 0.402283801532 Henry Cohn, 2025.
8 83 0.405303858040 Henry Cohn, 2026.
8 84 0.405612978673 Henry Cohn, 2026.
8 85 0.413778833762 Henry Cohn, 2025.
8 86 0.416857867243 Henry Cohn, 2026, needs more optimization.
8 88 0.418782717642 J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment. Math. 5 (1996), 139–159, https://projecteuclid.org/euclid.em/1047565645.
32⁢x3−8⁢x+1
8 89 0.421249110346 Henry Cohn, 2026.
8 90 0.422389551109 Henry Cohn, 2026.
8 91 0.423510643961 Henry Cohn, 2026.
8 92 0.424439081882 Henry Cohn, 2026, needs more optimization.
8 93 0.425292960391 Henry Cohn, 2026.
8 94 0.425630619041 Henry Cohn, 2026, needs more optimization.
8 95 0.426690121416 Henry Cohn, 2026, needs more optimization.
8 96 0.427525768702 Henry Cohn, 2026, needs more optimization.
8 97 0.428526010827 Henry Cohn, 2025.
8 99 0.428564490087 Henry Cohn, 2025.
8 100 0.428571420298 Henry Cohn, 2026, needs more optimization.
8 101 0.428571428376 Henry Cohn, 2026, needs more optimization.
8 114 0.428571428572 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−3
8 115 0.447648896804 Henry Cohn, 2026, needs more optimization.
8 116 0.448022446705 Henry Cohn, 2026, needs more optimization.
8 117 0.451867492073 Henry Cohn, 2026, needs more optimization.
8 118 0.455382682228 Henry Cohn, 2026.
8 119 0.461439500217 Henry Cohn, 2026, needs more optimization.
8 121 0.461848100275 Henry Cohn, 2026, needs more optimization.
8 136 0.462585942982 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
68⁢x2−12⁢x−9
8 137 0.466199226032 Henry Cohn, 2025.
8 138 0.468486456439 Henry Cohn, 2026, needs more optimization.
8 139 0.468833090621 Henry Cohn, 2026, needs more optimization.
8 140 0.470970373659 Henry Cohn, 2026, needs more optimization.
8 141 0.472529493835 Henry Cohn, 2026, needs more optimization.
8 143 0.476795268384 Henry Cohn, 2026, needs more optimization.
8 144 0.485247490489 Henry Cohn, 2026, needs more optimization.
8 145 0.487096769253 Henry Cohn, 2026, needs more optimization.
8 146 0.488646099141 Henry Cohn, 2026, needs more optimization.
8 147 0.488726765657 Henry Cohn, 2026, needs more optimization.
8 148 0.489575081016 Henry Cohn, 2026, needs more optimization.
8 149 0.489728906081 Henry Cohn, 2026, needs more optimization.
8 150 0.489754949602 Henry Cohn, 2026, needs more optimization.
8 151 0.490701500207 Henry Cohn, 2026, needs more optimization.
8 152 0.491613519779 Henry Cohn, 2026, needs more optimization.
8 153 0.492433667672 Henry Cohn, 2026, needs more optimization.
8 154 0.492684895854 Henry Cohn, 2026, needs more optimization.
8 155 0.493301058480 Henry Cohn, 2026, needs more optimization.
8 156 0.494129971018 Henry Cohn, 2026, needs more optimization.
8 157 0.494372949940 Henry Cohn, 2026, needs more optimization.
8 158 0.494814853408 Henry Cohn, 2026, needs more optimization.
8 159 0.495415668269 Henry Cohn, 2026, needs more optimization.
8 160 0.496361047090 Henry Cohn, 2026, needs more optimization.
8 162 0.496914471295 Henry Cohn, 2026, needs more optimization.
8 164 0.497382420937 Henry Cohn, 2026, needs more optimization.
8 166 0.497613945133 Henry Cohn, 2026, needs more optimization.
8 167 0.498497861414 Henry Cohn, 2026, needs more optimization.
8 170 0.499507408553 Henry Cohn, 2026, needs more optimization.
8 171 0.499928111996 Henry Cohn, 2026, needs more optimization.
8 240* 0.5 A. Korkine and G. Zolotareff, Sur les formes quadratiques, Math. Ann. 6 (1873), 366–389, doi:10.1007/BF01442795; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421; A. M. Odlyzko and N. J. A. Sloane, New bounds on the number of unit spheres that can touch a unit sphere in n dimensions, J. Combin. Theory Ser. A 26 (1979), 210–214, doi:10.1016/0097-3165(79)90074-8.
2⁢x−1
8 241 0.539501901248 Henry Cohn, 2024, needs more optimization.
8 242 0.544322669198 Henry Cohn, 2025, needs more optimization.
8 243 0.547703296571 Henry Cohn, 2024, needs more optimization.
8 244 0.550045933654 Henry Cohn, 2026, needs more optimization.
8 245 0.553653350879 Henry Cohn, 2025, needs more optimization.
8 246 0.554250154231 Henry Cohn, 2026, needs more optimization.
8 247 0.555877591876 Henry Cohn, 2026, needs more optimization.
8 248 0.558077949649 Henry Cohn, 2025, needs more optimization.
8 249 0.559446693208 Henry Cohn, 2025, needs more optimization.
8 250 0.560899555304 Henry Cohn, 2026, needs more optimization.
8 251 0.562047246263 Henry Cohn, 2025, needs more optimization.
8 252 0.564084932721 Henry Cohn, 2025, needs more optimization.
8 253 0.564179734130 Henry Cohn, 2026, needs more optimization.
8 254 0.564446060757 Henry Cohn, 2026, needs more optimization.
8 255 0.564558725654 Henry Cohn, 2025, needs more optimization.
8 256 0.564930782139 Henry Cohn, 2026, needs more optimization.
8 257 0.565191770046 Henry Cohn, 2025, needs more optimization.
8 259 0.568921803026 Henry Cohn, 2025, needs more optimization.
8 260 0.570454503740 Henry Cohn, 2026, needs more optimization.
8 261 0.571550056509 Henry Cohn, 2026, needs more optimization.
8 262 0.572820528622 Henry Cohn, 2026, needs more optimization.
8 263 0.573886460433 Henry Cohn, 2026, needs more optimization.
8 264 0.575008884250 Henry Cohn, 2026, needs more optimization.
8 265 0.575339813754 Henry Cohn, 2026, needs more optimization.
8 266 0.575646354485 Henry Cohn, 2026, needs more optimization.
8 267 0.576779204505 Henry Cohn, 2026, needs more optimization.
8 268 0.576850517457 Henry Cohn, 2026, needs more optimization.
8 269 0.576933471753 Henry Cohn, 2026, needs more optimization.
8 270 0.578143903584 Henry Cohn, 2026, needs more optimization.
8 271 0.578167917269 Henry Cohn, 2026, needs more optimization.
8 272 0.579566810513 Henry Cohn, 2026, needs more optimization.
8 273 0.579679677940 Henry Cohn, 2026, needs more optimization.
8 274 0.580059677099 Henry Cohn, 2026, needs more optimization.
8 275 0.581581374637 Henry Cohn, 2026, needs more optimization.
8 279 0.582073972917 Henry Cohn, 2026, needs more optimization.
8 282 0.582626137844 Henry Cohn, 2026, needs more optimization.
8 283 0.584977149361 Henry Cohn, 2026, needs more optimization.
8 284 0.585015614463 Henry Cohn, 2026, needs more optimization.
8 285 0.585071005644 Henry Cohn, 2026, needs more optimization.
8 286 0.585871253791 Henry Cohn, 2026, needs more optimization.
8 287 0.585976173670 Henry Cohn, 2026, needs more optimization.
8 288 0.586253292883 Henry Cohn, 2026, needs more optimization.
8 289 0.586254842860 Henry Cohn, 2026, needs more optimization.
8 290 0.586715382525 Henry Cohn, 2026, needs more optimization.
8 291 0.587456824680 Henry Cohn, 2026, needs more optimization.
8 292 0.587532973195 Henry Cohn, 2026, needs more optimization.
8 293 0.590459812898 Henry Cohn, 2026, needs more optimization.
8 294 0.590524245112 Henry Cohn, 2026, needs more optimization.
8 295 0.590655382592 Henry Cohn, 2026, needs more optimization.
8 296 0.590656469336 Henry Cohn, 2026, needs more optimization.
8 297 0.590892429638 Henry Cohn, 2026, needs more optimization.
8 298 0.590895383586 Henry Cohn, 2026, needs more optimization.
8 300 0.590944913753 Henry Cohn, 2026, needs more optimization.
8 304 0.591537423177 Henry Cohn, 2026, needs more optimization.
8 308 0.591841300958 Henry Cohn, 2026, needs more optimization.
8 309 0.592250069302 Henry Cohn, 2026, needs more optimization.
8 310 0.592250069348 Henry Cohn, 2026, needs more optimization.
8 311 0.600392682840 Henry Cohn, 2025, needs more optimization.
8 312 0.600857275911 Henry Cohn, 2025, needs more optimization.
8 313 0.601247557345 Henry Cohn, 2025, needs more optimization.
8 314 0.601604875833 Henry Cohn, 2025, needs more optimization.
8 315 0.601754794772 Henry Cohn, 2025, needs more optimization.
8 316 0.601883016118 Henry Cohn, 2026, needs more optimization.
8 317 0.602304929605 Henry Cohn, 2025, needs more optimization.
8 318 0.604495111714 Henry Cohn, 2025, needs more optimization.
8 319 0.604822638198 Henry Cohn, 2025, needs more optimization.
8 320 0.605769909395 Henry Cohn, 2026, needs more optimization.
8 321 0.606080632890 Henry Cohn, 2025, needs more optimization.
8 322 0.606676646313 Henry Cohn, 2025, needs more optimization.
8 323 0.606748296967 Henry Cohn, 2025, needs more optimization.
8 325 0.606875669076 Henry Cohn, 2025, needs more optimization.
8 326 0.607207281517 Henry Cohn, 2025, needs more optimization.
8 327 0.608149701647 Henry Cohn, 2025, needs more optimization.
8 328 0.608181717009 Henry Cohn, 2026, needs more optimization.
8 329 0.608320338402 Henry Cohn, 2025, needs more optimization.
8 330 0.609064020319 Henry Cohn, 2025, needs more optimization.
8 331 0.609197149344 Henry Cohn, 2025, needs more optimization.
8 332 0.609790935425 Henry Cohn, 2025, needs more optimization.
8 333 0.609869023821 Henry Cohn, 2025, needs more optimization.
8 334 0.610018411770 Henry Cohn, 2025, needs more optimization.
8 335 0.610073776765 Henry Cohn, 2025, needs more optimization.
8 336 0.610729053233 Henry Cohn, 2026, needs more optimization.
8 337 0.610839137829 Henry Cohn, 2025, needs more optimization.
8 338 0.611612890703 Henry Cohn, 2025, needs more optimization.
8 340 0.611870699584 Henry Cohn, 2026, needs more optimization.
8 341 0.612146643052 Henry Cohn, 2025, needs more optimization.
8 342 0.612148803025 Henry Cohn, 2025, needs more optimization.
8 343 0.612154038153 Henry Cohn, 2025, needs more optimization.
8 344 0.612780479272 Henry Cohn, 2026, needs more optimization.
8 345 0.612945172261 Henry Cohn, 2025, needs more optimization.
8 346 0.613013252673 Henry Cohn, 2026, needs more optimization.
8 348 0.613901448115 Henry Cohn, 2025, needs more optimization.
8 349 0.613958393143 Henry Cohn, 2025, needs more optimization.
8 350 0.614081594495 Henry Cohn, 2025, needs more optimization.
8 351 0.614693773399 Henry Cohn, 2025, needs more optimization.
8 352 0.615043453221 Henry Cohn, 2026, needs more optimization.
8 353 0.615891488252 Henry Cohn, 2025, needs more optimization.
8 354 0.616147123726 Henry Cohn, 2025, needs more optimization.
8 355 0.616343028699 Henry Cohn, 2025, needs more optimization.
8 356 0.616552318905 Henry Cohn, 2025, needs more optimization.
8 357 0.616557922801 Henry Cohn, 2025, needs more optimization.
8 358 0.616753657402 Henry Cohn, 2025, needs more optimization.
8 359 0.617239684539 Henry Cohn, 2025, needs more optimization.
8 360 0.617327508249 Henry Cohn, 2026, needs more optimization.
8 361 0.617622312575 Henry Cohn, 2025, needs more optimization.
8 363 0.618218429962 Henry Cohn, 2025, needs more optimization.
8 364 0.618861448418 Henry Cohn, 2026, needs more optimization.
8 365 0.618946330794 Henry Cohn, 2025, needs more optimization.
8 366 0.619533958360 Henry Cohn, 2025, needs more optimization.
8 367 0.619566098791 Henry Cohn, 2025, needs more optimization.
8 368 0.620019189187 Henry Cohn, 2025, needs more optimization.
8 369 0.620799329733 Henry Cohn, 2025, needs more optimization.
8 370 0.621212628217 Henry Cohn, 2025, needs more optimization.
8 371 0.621219399291 Henry Cohn, 2025, needs more optimization.
8 372 0.621278546847 Henry Cohn, 2025, needs more optimization.
8 373 0.621439323831 Henry Cohn, 2025, needs more optimization.
8 374 0.621809961723 Henry Cohn, 2025, needs more optimization.
8 375 0.622680026091 Henry Cohn, 2025, needs more optimization.
8 376 0.622721928823 Henry Cohn, 2026, needs more optimization.
8 377 0.623361057450 Henry Cohn, 2025, needs more optimization.
8 378 0.623375974656 Henry Cohn, 2025, needs more optimization.
8 379 0.623561181724 Henry Cohn, 2025, needs more optimization.
8 380 0.623729549220 Henry Cohn, 2026, needs more optimization.
8 381 0.624750658484 Henry Cohn, 2025, needs more optimization.
8 382 0.624770012520 Henry Cohn, 2025, needs more optimization.
8 383 0.624991249003 Henry Cohn, 2025, needs more optimization.
8 384 0.625403316793 Henry Cohn, 2025, needs more optimization.
8 385 0.625724677010 Henry Cohn, 2025, needs more optimization.
8 386 0.626127695908 Henry Cohn, 2025, needs more optimization.
8 388 0.626432231530 Henry Cohn, 2025, needs more optimization.
8 389 0.626962564375 Henry Cohn, 2025, needs more optimization.
8 390 0.627640882088 Henry Cohn, 2025, needs more optimization.
8 391 0.628205858700 Henry Cohn, 2025, needs more optimization.
8 392 0.628294232678 Henry Cohn, 2025, needs more optimization.
8 393 0.628396377236 Henry Cohn, 2025, needs more optimization.
8 394 0.628399885301 Henry Cohn, 2025, needs more optimization.
8 395 0.628659533842 Henry Cohn, 2025, needs more optimization.
8 396 0.629105201649 Henry Cohn, 2025, needs more optimization.
8 397 0.629169317910 Henry Cohn, 2025, needs more optimization.
8 398 0.629882033172 Henry Cohn, 2025, needs more optimization.
8 399 0.629897232379 Henry Cohn, 2025, needs more optimization.
8 400 0.630174839577 Henry Cohn, 2025, needs more optimization.
8 401 0.631382584291 Henry Cohn, 2025, needs more optimization.
8 402 0.631390153886 Henry Cohn, 2025, needs more optimization.
8 403 0.631491811937 Henry Cohn, 2025, needs more optimization.
8 404 0.631523250496 Henry Cohn, 2025, needs more optimization.
8 405 0.632217833561 Henry Cohn, 2025, needs more optimization.
8 406 0.632349801223 Henry Cohn, 2025, needs more optimization.
8 407 0.632398200978 Henry Cohn, 2025, needs more optimization.
8 408 0.632751021452 Henry Cohn, 2025, needs more optimization.
8 409 0.632771125197 Henry Cohn, 2025, needs more optimization.
8 410 0.633663719121 Henry Cohn, 2025, needs more optimization.
8 411 0.633684274566 Henry Cohn, 2025, needs more optimization.
8 412 0.634038324108 Henry Cohn, 2025, needs more optimization.
8 413 0.634054592998 Henry Cohn, 2025, needs more optimization.
8 414 0.634320629040 Henry Cohn, 2025, needs more optimization.
8 415 0.634728376576 Henry Cohn, 2025, needs more optimization.
8 416 0.634814438444 Henry Cohn, 2025, needs more optimization.
8 417 0.634837438867 Henry Cohn, 2025, needs more optimization.
8 418 0.634934621158 Henry Cohn, 2025, needs more optimization.
8 419 0.635070107909 Henry Cohn, 2025, needs more optimization.
8 420 0.635468466546 Henry Cohn, 2026, needs more optimization.
8 421 0.636141198917 Henry Cohn, 2025, needs more optimization.
8 423 0.636176710499 Henry Cohn, 2025, needs more optimization.
8 424 0.636318728782 Henry Cohn, 2026, needs more optimization.
8 425 0.637001897162 Henry Cohn, 2025, needs more optimization.
8 426 0.637023119393 Henry Cohn, 2025, needs more optimization.
8 427 0.637087408572 Henry Cohn, 2025, needs more optimization.
8 428 0.637089357587 Henry Cohn, 2025, needs more optimization.
8 429 0.637091035838 Henry Cohn, 2025, needs more optimization.
8 430 0.637597366016 Henry Cohn, 2025, needs more optimization.
8 431 0.637929976400 Henry Cohn, 2026, needs more optimization.
8 432 0.638116238897 Henry Cohn, 2025, needs more optimization.
8 433 0.638534297751 Henry Cohn, 2025, needs more optimization.
8 434 0.638897270433 Henry Cohn, 2025, needs more optimization.
8 435 0.639069879825 Henry Cohn, 2025, needs more optimization.
8 436 0.639792064682 Henry Cohn, 2025, needs more optimization.
8 437 0.639809402862 Henry Cohn, 2025, needs more optimization.
8 438 0.640047960605 Henry Cohn, 2025, needs more optimization.
8 439 0.640157825639 Henry Cohn, 2025, needs more optimization.
8 440 0.640469991884 Henry Cohn, 2025, needs more optimization.
8 441 0.640506385547 Henry Cohn, 2025, needs more optimization.
8 443 0.640766099500 Henry Cohn, 2025, needs more optimization.
8 445 0.641262965109 Henry Cohn, 2025, needs more optimization.
8 446 0.641438529490 Henry Cohn, 2025, needs more optimization.
8 447 0.641482891413 Henry Cohn, 2025, needs more optimization.
8 448 0.641496880893 Henry Cohn, 2025, needs more optimization.
8 449 0.641578861091 Henry Cohn, 2025, needs more optimization.
8 450 0.641641003734 Henry Cohn, 2025, needs more optimization.
8 451 0.641797750053 Henry Cohn, 2025, needs more optimization.
8 452 0.641811557867 Henry Cohn, 2025, needs more optimization.
8 453 0.641908870744 Henry Cohn, 2025, needs more optimization.
8 454 0.641978565813 Henry Cohn, 2025, needs more optimization.
8 455 0.642174437296 Henry Cohn, 2025, needs more optimization.
8 456 0.642217378185 Henry Cohn, 2025, needs more optimization.
8 457 0.642229200426 Henry Cohn, 2025, needs more optimization.
8 458 0.642270284839 Henry Cohn, 2025, needs more optimization.
8 459 0.642632119105 Henry Cohn, 2025, needs more optimization.
8 460 0.643398235197 Henry Cohn, 2026, needs more optimization.
8 461 0.643491563350 Henry Cohn, 2025, needs more optimization.
8 462 0.643496044258 Henry Cohn, 2025, needs more optimization.
8 463 0.643541281167 Henry Cohn, 2025, needs more optimization.
8 464 0.643549393561 Henry Cohn, 2025, needs more optimization.
8 465 0.643579577026 Henry Cohn, 2025, needs more optimization.
8 466 0.643718584379 Henry Cohn, 2025, needs more optimization.
8 467 0.643732809840 Henry Cohn, 2025, needs more optimization.
8 468 0.644388241331 Henry Cohn, 2026, needs more optimization.
8 469 0.644393228166 Henry Cohn, 2025, needs more optimization.
8 470 0.644461578333 Henry Cohn, 2025, needs more optimization.
8 471 0.645133996535 Henry Cohn, 2025, needs more optimization.
8 472 0.645158393914 Henry Cohn, 2025, needs more optimization.
8 473 0.645195224081 Henry Cohn, 2025, needs more optimization.
8 474 0.645247851108 Henry Cohn, 2025, needs more optimization.
8 475 0.645262692751 Henry Cohn, 2025, needs more optimization.
8 476 0.646060671921 Henry Cohn, 2026, needs more optimization.
8 477 0.646072431746 Henry Cohn, 2025, needs more optimization.
8 478 0.646125842259 Henry Cohn, 2025, needs more optimization.
8 479 0.647189050236 Henry Cohn, 2025, needs more optimization.
8 480 0.648172971263 Henry Cohn, 2026, needs more optimization.
8 481 0.648203278480 Henry Cohn, 2025, needs more optimization.
8 482 0.648231152639 Henry Cohn, 2025, needs more optimization.
8 483 0.648257524986 Henry Cohn, 2025, needs more optimization.
8 484 0.648301006016 Henry Cohn, 2025, needs more optimization.
8 485 0.648304156375 Henry Cohn, 2025, needs more optimization.
8 486 0.648379802504 Henry Cohn, 2025, needs more optimization.
8 488 0.648409107473 Henry Cohn, 2025, needs more optimization.
8 489 0.648878574511 Henry Cohn, 2025, needs more optimization.
8 491 0.648969005235 Henry Cohn, 2025, needs more optimization.
8 492 0.649044714764 Henry Cohn, 2026, needs more optimization.
8 495 0.649395489506 Henry Cohn, 2025, needs more optimization.
8 496 0.650342450429 Henry Cohn, 2026, needs more optimization.
8 497 0.650460855550 Henry Cohn, 2026, needs more optimization.
8 498 0.651812874290 Henry Cohn, 2025, needs more optimization.
8 499 0.651821743715 Henry Cohn, 2025, needs more optimization.
8 500 0.651864776838 Henry Cohn, 2025, needs more optimization.
8 501 0.651903079136 Henry Cohn, 2025, needs more optimization.
8 504 0.651983459840 Henry Cohn, 2026, needs more optimization.
8 506 0.652606806992 Henry Cohn, 2025, needs more optimization.
8 508 0.652625400184 Henry Cohn, 2026, needs more optimization.
8 509 0.652692843143 Henry Cohn, 2025, needs more optimization.
8 510 0.652761675344 Henry Cohn, 2025, needs more optimization.
8 511 0.653822844364 Henry Cohn, 2025, needs more optimization.
8 512 0.653824945416 Henry Cohn, 2025, needs more optimization.
8 513 0.653916433203 Henry Cohn, 2025, needs more optimization.
8 514 0.653949826228 Henry Cohn, 2025, needs more optimization.
8 515 0.653957938818 Henry Cohn, 2025, needs more optimization.
8 517 0.654161754594 Henry Cohn, 2025, needs more optimization.
8 519 0.654636126810 Henry Cohn, 2025, needs more optimization.
8 520 0.655352966131 Henry Cohn, 2025, needs more optimization.
8 522 0.655378986905 Henry Cohn, 2025, needs more optimization.
8 523 0.655409138883 Henry Cohn, 2025, needs more optimization.
8 524 0.655432550572 Henry Cohn, 2025, needs more optimization.
8 526 0.656607371810 Henry Cohn, 2025, needs more optimization.
8 528 0.656622819844 Henry Cohn, 2026, needs more optimization.
8 529 0.656662772223 Henry Cohn, 2025, needs more optimization.
8 530 0.656667219490 Henry Cohn, 2025, needs more optimization.
8 531 0.656677786317 Henry Cohn, 2025, needs more optimization.
8 532 0.656705658565 Henry Cohn, 2026, needs more optimization.
8 534 0.656816987118 Henry Cohn, 2025, needs more optimization.
8 535 0.657707828098 Henry Cohn, 2025, needs more optimization.
8 536 0.657712569744 Henry Cohn, 2025, needs more optimization.
8 537 0.657727538788 Henry Cohn, 2025, needs more optimization.
8 538 0.657963683933 Henry Cohn, 2026, needs more optimization.
8 539 0.659017871832 Henry Cohn, 2025, needs more optimization.
8 540 0.659064677191 Henry Cohn, 2026, needs more optimization.
8 541 0.659074917342 Henry Cohn, 2025, needs more optimization.
8 542 0.659268935193 Henry Cohn, 2025, needs more optimization.
8 543 0.660020360645 Henry Cohn, 2025, needs more optimization.
8 544 0.660026024022 Henry Cohn, 2025, needs more optimization.
8 545 0.660034658104 Henry Cohn, 2025, needs more optimization.
8 546 0.660039231384 Henry Cohn, 2025, needs more optimization.
8 547 0.660052739108 Henry Cohn, 2025, needs more optimization.
8 548 0.660077488246 Henry Cohn, 2026, needs more optimization.
8 551 0.660974086809 Henry Cohn, 2025, needs more optimization.
8 552 0.660987073712 Henry Cohn, 2025, needs more optimization.
8 553 0.661549468537 Henry Cohn, 2025, needs more optimization.
8 554 0.661937000088 Henry Cohn, 2025, needs more optimization.
8 555 0.661938005024 Henry Cohn, 2025, needs more optimization.
8 556 0.661961369488 Henry Cohn, 2025, needs more optimization.
8 557 0.662037705835 Henry Cohn, 2025, needs more optimization.
8 558 0.662468653075 Henry Cohn, 2025, needs more optimization.
8 561 0.662973680970 Henry Cohn, 2025, needs more optimization.
8 563 0.663021420021 Henry Cohn, 2025, needs more optimization.
8 564 0.663029029492 Henry Cohn, 2025, needs more optimization.
8 565 0.663035818985 Henry Cohn, 2025, needs more optimization.
8 566 0.663101282161 Henry Cohn, 2025, needs more optimization.
8 567 0.663892412862 Henry Cohn, 2025, needs more optimization.
8 568 0.663926371318 Henry Cohn, 2025, needs more optimization.
8 569 0.664046024545 Henry Cohn, 2025, needs more optimization.
8 570 0.664623961042 Henry Cohn, 2025, needs more optimization.
8 571 0.664637068515 Henry Cohn, 2025, needs more optimization.
8 572 0.664702818723 Henry Cohn, 2026, needs more optimization.
8 576 0.665248884435 Henry Cohn, 2026, needs more optimization.
8 580 0.665302826327 Henry Cohn, 2026, needs more optimization.
8 581 0.665350887801 Henry Cohn, 2025, needs more optimization.
8 584 0.665379649120 Henry Cohn, 2025, needs more optimization.
8 586 0.665380549827 Henry Cohn, 2025, needs more optimization.
8 587 0.665435047722 Henry Cohn, 2025, needs more optimization.
8 588 0.665445319204 Henry Cohn, 2025, needs more optimization.
8 592 0.665561282339 Henry Cohn, 2025, needs more optimization.
8 594 0.666130895250 Henry Cohn, 2026, needs more optimization.
8 595 0.666130895254 Henry Cohn, 2025, needs more optimization.
8 596 0.666387024705 Henry Cohn, 2025, needs more optimization.
8 599 0.666397358052 Henry Cohn, 2025, needs more optimization.
8 600 0.666602509895 Henry Cohn, 2026, needs more optimization.
8 601 0.666965063068 Henry Cohn, 2025, needs more optimization.
8 603 0.666985574341 Henry Cohn, 2025, needs more optimization.
8 604 0.667055396755 Henry Cohn, 2026, needs more optimization.
8 605 0.667060658637 Henry Cohn, 2025, needs more optimization.
8 606 0.667072130559 Henry Cohn, 2025, needs more optimization.
8 607 0.667087479684 Henry Cohn, 2025, needs more optimization.
8 608 0.667089302599 Henry Cohn, 2025, needs more optimization.
8 609 0.667095398399 Henry Cohn, 2025, needs more optimization.
8 610 0.667099364039 Henry Cohn, 2025, needs more optimization.
8 611 0.667108979091 Henry Cohn, 2025, needs more optimization.
8 613 0.667111574246 Henry Cohn, 2025, needs more optimization.
8 614 0.667138324876 Henry Cohn, 2025, needs more optimization.
8 615 0.667483585956 Henry Cohn, 2025, needs more optimization.
8 616 0.667623615616 Henry Cohn, 2025, needs more optimization.
8 617 0.667658585372 Henry Cohn, 2025, needs more optimization.
8 618 0.667665939580 Henry Cohn, 2025, needs more optimization.
8 620 0.667678310990 Henry Cohn, 2025, needs more optimization.
8 621 0.667691025236 Henry Cohn, 2025, needs more optimization.
8 622 0.667692412190 Henry Cohn, 2025, needs more optimization.
8 623 0.667736479972 Henry Cohn, 2025, needs more optimization.
8 624 0.667737235348 Henry Cohn, 2025, needs more optimization.
8 625 0.667790082788 Henry Cohn, 2025, needs more optimization.
8 626 0.667856165492 Henry Cohn, 2025, needs more optimization.
8 628 0.667862843031 Henry Cohn, 2026, needs more optimization.
8 632 0.667996157491 Henry Cohn, 2026, needs more optimization.
8 633 0.668028469835 Henry Cohn, 2025, needs more optimization.
8 634 0.668098972215 Henry Cohn, 2025, needs more optimization.
8 635 0.668103995122 Henry Cohn, 2025, needs more optimization.
8 636 0.668296451526 Henry Cohn, 2026, needs more optimization.
8 637 0.668744675880 Henry Cohn, 2025, needs more optimization.
8 638 0.668765396908 Henry Cohn, 2025, needs more optimization.
8 639 0.668781500950 Henry Cohn, 2025, needs more optimization.
8 640 0.668796717281 Henry Cohn, 2026, needs more optimization.
8 641 0.668821436898 Henry Cohn, 2025, needs more optimization.
8 643 0.668849763782 Henry Cohn, 2025, needs more optimization.
8 644 0.668888933796 Henry Cohn, 2026, needs more optimization.
8 645 0.668913424501 Henry Cohn, 2025, needs more optimization.
8 646 0.668925108447 Henry Cohn, 2025, needs more optimization.
8 648 0.670118418002 Henry Cohn, 2025, needs more optimization.
8 649 0.670137153286 Henry Cohn, 2025, needs more optimization.
8 651 0.670169070821 Henry Cohn, 2025, needs more optimization.
8 652 0.670175947064 Henry Cohn, 2025, needs more optimization.
8 653 0.670249265653 Henry Cohn, 2025, needs more optimization.
8 654 0.670496836573 Henry Cohn, 2025, needs more optimization.
8 656 0.670540356874 Henry Cohn, 2025, needs more optimization.
8 657 0.670625558936 Henry Cohn, 2026, needs more optimization.
8 658 0.670943098239 Henry Cohn, 2026, needs more optimization.
8 660 0.671405900252 Henry Cohn, 2026, needs more optimization.
8 661 0.671576063393 Henry Cohn, 2026, needs more optimization.
8 662 0.672361517486 Henry Cohn, 2025, needs more optimization.
8 663 0.672376082884 Henry Cohn, 2025, needs more optimization.
8 664 0.672381833357 Henry Cohn, 2025, needs more optimization.
8 665 0.672388136782 Henry Cohn, 2025, needs more optimization.
8 668 0.672402986964 Henry Cohn, 2025, needs more optimization.
8 669 0.672405478766 Henry Cohn, 2025, needs more optimization.
8 671 0.672433821191 Henry Cohn, 2025, needs more optimization.
8 673 0.672444029762 Henry Cohn, 2025, needs more optimization.
8 674 0.672920393834 Henry Cohn, 2025, needs more optimization.
8 675 0.673610862017 Henry Cohn, 2025, needs more optimization.
8 676 0.673615460560 Henry Cohn, 2025, needs more optimization.
8 677 0.673654129403 Henry Cohn, 2025, needs more optimization.
8 678 0.673656323795 Henry Cohn, 2025, needs more optimization.
8 681 0.673674600224 Henry Cohn, 2025, needs more optimization.
8 682 0.673708965600 Henry Cohn, 2025, needs more optimization.
8 683 0.676263648596 Henry Cohn, 2025, needs more optimization.
8 684 0.676421990904 Henry Cohn, 2026, needs more optimization.
8 685 0.677531018202 Henry Cohn, 2025, needs more optimization.
8 686 0.677544477572 Henry Cohn, 2025, needs more optimization.
8 687 0.677555611920 Henry Cohn, 2025, needs more optimization.
8 689 0.677559094580 Henry Cohn, 2025, needs more optimization.
8 690 0.677573227978 Henry Cohn, 2025, needs more optimization.
8 691 0.677899660426 Henry Cohn, 2025, needs more optimization.
8 692 0.678679769647 Henry Cohn, 2025, needs more optimization.
8 693 0.678688084707 Henry Cohn, 2025, needs more optimization.
8 694 0.678720290855 Henry Cohn, 2025, needs more optimization.
8 695 0.678729793454 Henry Cohn, 2025, needs more optimization.
8 696 0.678735778078 Henry Cohn, 2025, needs more optimization.
8 697 0.678782198352 Henry Cohn, 2025, needs more optimization.
8 698 0.678784004008 Henry Cohn, 2025, needs more optimization.
8 700 0.679658794379 Henry Cohn, 2025, needs more optimization.
8 701 0.680815834525 Henry Cohn, 2025, needs more optimization.
8 702 0.680825164121 Henry Cohn, 2025, needs more optimization.
8 704 0.680860712448 Henry Cohn, 2025, needs more optimization.
8 705 0.681761519941 Henry Cohn, 2025, needs more optimization.
8 706 0.681769565159 Henry Cohn, 2026, needs more optimization.
8 707 0.681783437957 Henry Cohn, 2025, needs more optimization.
8 708 0.681790375821 Henry Cohn, 2025, needs more optimization.
8 709 0.681807845025 Henry Cohn, 2025, needs more optimization.
8 710 0.681819621502 Henry Cohn, 2025, needs more optimization.
8 711 0.682547829724 Henry Cohn, 2025, needs more optimization.
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8 713 0.682631957791 Henry Cohn, 2025, needs more optimization.
8 714 0.682647104955 Henry Cohn, 2025, needs more optimization.
8 715 0.682724276874 Henry Cohn, 2025, needs more optimization.
8 716 0.683299678822 Henry Cohn, 2025, needs more optimization.
8 717 0.683347815941 Henry Cohn, 2025, needs more optimization.
8 718 0.684191236637 Henry Cohn, 2025, needs more optimization.
8 720 0.684198725768 Henry Cohn, 2025, needs more optimization.
8 721 0.684209256236 Henry Cohn, 2025, needs more optimization.
8 722 0.684552996041 Henry Cohn, 2025, needs more optimization.
8 723 0.684597203485 Henry Cohn, 2025, needs more optimization.
8 725 0.685637290899 Henry Cohn, 2025, needs more optimization.
8 727 0.685651013687 Henry Cohn, 2025, needs more optimization.
8 728 0.686655440089 Henry Cohn, 2025, needs more optimization.
8 730 0.686764596522 Henry Cohn, 2025, needs more optimization.
8 731 0.687195507005 Henry Cohn, 2025, needs more optimization.
8 732 0.687199858892 Henry Cohn, 2025, needs more optimization.
8 733 0.687556618604 Henry Cohn, 2025, needs more optimization.
8 734 0.687560122508 Henry Cohn, 2025, needs more optimization.
8 735 0.687565651641 Henry Cohn, 2025, needs more optimization.
8 736 0.687595156374 Henry Cohn, 2025, needs more optimization.
8 737 0.688320161391 Henry Cohn, 2025, needs more optimization.
8 738 0.688324275861 Henry Cohn, 2026, needs more optimization.
8 739 0.688340073834 Henry Cohn, 2025, needs more optimization.
8 741 0.688352439514 Henry Cohn, 2025, needs more optimization.
8 742 0.688380495694 Henry Cohn, 2026, needs more optimization.
8 743 0.689087386175 Henry Cohn, 2025, needs more optimization.
8 744 0.689093364046 Henry Cohn, 2025, needs more optimization.
8 745 0.689245371248 Henry Cohn, 2025, needs more optimization.
8 746 0.689257208969 Henry Cohn, 2025, needs more optimization.
8 747 0.689285686948 Henry Cohn, 2025, needs more optimization.
8 748 0.689650119683 Henry Cohn, 2025, needs more optimization.
8 749 0.689654681524 Henry Cohn, 2025, needs more optimization.
8 750 0.689712410927 Henry Cohn, 2026, needs more optimization.
8 751 0.689712820395 Henry Cohn, 2025, needs more optimization.
8 753 0.690221625290 Henry Cohn, 2025, needs more optimization.
8 754 0.690249738820 Henry Cohn, 2025, needs more optimization.
8 756 0.690254002412 Henry Cohn, 2025, needs more optimization.
8 757 0.690262706824 Henry Cohn, 2025, needs more optimization.
8 758 0.690269097024 Henry Cohn, 2025, needs more optimization.
8 760 0.690275149052 Henry Cohn, 2025, needs more optimization.
8 761 0.690423995807 Henry Cohn, 2025, needs more optimization.
8 762 0.690931028446 Henry Cohn, 2025, needs more optimization.
8 763 0.690985339857 Henry Cohn, 2025, needs more optimization.
8 764 0.691649582708 Henry Cohn, 2025, needs more optimization.
8 765 0.691657242200 Henry Cohn, 2025, needs more optimization.
8 766 0.691660459895 Henry Cohn, 2025, needs more optimization.
8 767 0.691733318685 Henry Cohn, 2025, needs more optimization.
8 768 0.691738086675 Henry Cohn, 2025, needs more optimization.
8 770 0.691756855104 Henry Cohn, 2025, needs more optimization.
8 771 0.691764059186 Henry Cohn, 2025, needs more optimization.
8 772 0.691769701878 Henry Cohn, 2025, needs more optimization.
8 773 0.692188715910 Henry Cohn, 2025, needs more optimization.
8 774 0.692427638048 Henry Cohn, 2025, needs more optimization.
8 775 0.692465210450 Henry Cohn, 2025, needs more optimization.
8 776 0.692503031109 Henry Cohn, 2026, needs more optimization.
8 777 0.692507780945 Henry Cohn, 2025, needs more optimization.
8 778 0.692685446443 Henry Cohn, 2025, needs more optimization.
8 779 0.692696406897 Henry Cohn, 2025, needs more optimization.
8 780 0.692703051394 Henry Cohn, 2025, needs more optimization.
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8 782 0.692758858442 Henry Cohn, 2025, needs more optimization.
8 783 0.692780451895 Henry Cohn, 2025, needs more optimization.
8 784 0.692817786168 Henry Cohn, 2025, needs more optimization.
8 785 0.693746730553 Henry Cohn, 2025, needs more optimization.
8 786 0.693749065175 Henry Cohn, 2025, needs more optimization.
8 787 0.693809101014 Henry Cohn, 2025, needs more optimization.
8 788 0.693820391069 Henry Cohn, 2025, needs more optimization.
8 789 0.694271052652 Henry Cohn, 2025, needs more optimization.
8 790 0.694297113974 Henry Cohn, 2025, needs more optimization.
8 791 0.694304362807 Henry Cohn, 2025, needs more optimization.
8 792 0.694317963429 Henry Cohn, 2025, needs more optimization.
8 794 0.694664633550 Henry Cohn, 2025, needs more optimization.
8 795 0.694703983569 Henry Cohn, 2025, needs more optimization.
8 797 0.694715522952 Henry Cohn, 2025, needs more optimization.
8 799 0.694912235139 Henry Cohn, 2025, needs more optimization.
8 800 0.695331096435 Henry Cohn, 2025, needs more optimization.
8 801 0.695383678268 Henry Cohn, 2025, needs more optimization.
8 802 0.695653080170 Henry Cohn, 2025, needs more optimization.
8 803 0.695703246342 Henry Cohn, 2025, needs more optimization.
8 804 0.696078886015 Henry Cohn, 2025, needs more optimization.
8 805 0.696404294257 Henry Cohn, 2025, needs more optimization.
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8 809 0.696493755900 Henry Cohn, 2025, needs more optimization.
8 810 0.696521885117 Henry Cohn, 2026, needs more optimization.
8 811 0.696772294525 Henry Cohn, 2025, needs more optimization.
8 812 0.696772875652 Henry Cohn, 2025, needs more optimization.
8 813 0.696926164631 Henry Cohn, 2025, needs more optimization.
8 814 0.697612546310 Henry Cohn, 2025, needs more optimization.
8 815 0.697613780682 Henry Cohn, 2025, needs more optimization.
8 817 0.697625402129 Henry Cohn, 2025, needs more optimization.
8 818 0.697635270970 Henry Cohn, 2025, needs more optimization.
8 819 0.697656849098 Henry Cohn, 2025, needs more optimization.
8 820 0.697735882156 Henry Cohn, 2025, needs more optimization.
8 821 0.697770280526 Henry Cohn, 2025, needs more optimization.
8 822 0.698090630860 Henry Cohn, 2026, needs more optimization.
8 823 0.698109445083 Henry Cohn, 2025, needs more optimization.
8 824 0.698158922001 Henry Cohn, 2025, needs more optimization.
8 825 0.698171458389 Henry Cohn, 2025, needs more optimization.
8 826 0.698267233858 Henry Cohn, 2025, needs more optimization.
8 828 0.698680526523 Henry Cohn, 2025, needs more optimization.
8 829 0.698698277435 Henry Cohn, 2025, needs more optimization.
8 833 0.699228866288 Henry Cohn, 2025, needs more optimization.
8 834 0.699236866590 Henry Cohn, 2025, needs more optimization.
8 835 0.699541731401 Henry Cohn, 2025, needs more optimization.
8 838 0.699976879270 Henry Cohn, 2025, needs more optimization.
8 839 0.699989920786 Henry Cohn, 2025, needs more optimization.
8 840 0.700052149297 Henry Cohn, 2025, needs more optimization.
8 842 0.700535494509 Henry Cohn, 2026, needs more optimization.
8 844 0.700579575605 Henry Cohn, 2025, needs more optimization.
8 846 0.700582454670 Henry Cohn, 2025, needs more optimization.
8 847 0.700585511073 Henry Cohn, 2025, needs more optimization.
8 848 0.700783071915 Henry Cohn, 2026, needs more optimization.
8 850 0.701194373603 Henry Cohn, 2025, needs more optimization.
8 851 0.701205442734 Henry Cohn, 2025, needs more optimization.
8 852 0.701300853845 Henry Cohn, 2025, needs more optimization.
8 853 0.701627111266 Henry Cohn, 2025, needs more optimization.
8 854 0.701647154743 Henry Cohn, 2025, needs more optimization.
8 856 0.702140146489 Henry Cohn, 2025, needs more optimization.
8 857 0.702140752693 Henry Cohn, 2025, needs more optimization.
8 858 0.702158024689 Henry Cohn, 2026, needs more optimization.
8 859 0.702369007300 Henry Cohn, 2025, needs more optimization.
8 860 0.702635130955 Henry Cohn, 2026, needs more optimization.
8 861 0.702639415712 Henry Cohn, 2025, needs more optimization.
8 862 0.703046881118 Henry Cohn, 2026, needs more optimization.
8 863 0.703047455658 Henry Cohn, 2025, needs more optimization.
8 864 0.703075542271 Henry Cohn, 2025, needs more optimization.
8 865 0.703086668407 Henry Cohn, 2025, needs more optimization.
8 866 0.703089439857 Henry Cohn, 2025, needs more optimization.
8 868 0.703400832635 Henry Cohn, 2025, needs more optimization.
8 870 0.703489788978 Henry Cohn, 2026, needs more optimization.
8 871 0.703728936164 Henry Cohn, 2025, needs more optimization.
8 872 0.703743378781 Henry Cohn, 2026, needs more optimization.
8 873 0.703890487142 Henry Cohn, 2025, needs more optimization.
8 874 0.703929272417 Henry Cohn, 2025, needs more optimization.
8 875 0.703937923467 Henry Cohn, 2025, needs more optimization.
8 876 0.703952340476 Henry Cohn, 2025, needs more optimization.
8 877 0.704409953183 Henry Cohn, 2025, needs more optimization.
8 879 0.704413282221 Henry Cohn, 2025, needs more optimization.
8 880 0.704445046575 Henry Cohn, 2025, needs more optimization.
8 881 0.704454523140 Henry Cohn, 2025, needs more optimization.
8 882 0.704494807984 Henry Cohn, 2026, needs more optimization.
8 883 0.704812314689 Henry Cohn, 2025, needs more optimization.
8 884 0.704825256769 Henry Cohn, 2025, needs more optimization.
8 886 0.705062062139 Henry Cohn, 2025, needs more optimization.
8 887 0.705062193245 Henry Cohn, 2025, needs more optimization.
8 888 0.705070441205 Henry Cohn, 2025, needs more optimization.
8 889 0.705080235144 Henry Cohn, 2025, needs more optimization.
8 890 0.705113042198 Henry Cohn, 2025, needs more optimization.
8 891 0.705712899680 Henry Cohn, 2025, needs more optimization.
8 892 0.705721402518 Henry Cohn, 2025, needs more optimization.
8 893 0.705729660190 Henry Cohn, 2025, needs more optimization.
8 894 0.705734532374 Henry Cohn, 2025, needs more optimization.
8 895 0.705745173745 Henry Cohn, 2025, needs more optimization.
8 896 0.705761190193 Henry Cohn, 2025, needs more optimization.
8 897 0.705764606541 Henry Cohn, 2025, needs more optimization.
8 899 0.705821749669 Henry Cohn, 2025, needs more optimization.
8 902 0.705829679270 Henry Cohn, 2025, needs more optimization.
8 903 0.705835670346 Henry Cohn, 2025, needs more optimization.
8 904 0.706104844872 Henry Cohn, 2025, needs more optimization.
8 905 0.706106342062 Henry Cohn, 2025, needs more optimization.
8 908 0.706543218819 Henry Cohn, 2025, needs more optimization.
8 909 0.706548180413 Henry Cohn, 2025, needs more optimization.
8 910 0.706549815083 Henry Cohn, 2025, needs more optimization.
8 911 0.706561407014 Henry Cohn, 2025, needs more optimization.
8 914 0.706571631333 Henry Cohn, 2025, needs more optimization.
8 915 0.707004569607 Henry Cohn, 2025, needs more optimization.
8 916 0.707012136771 Henry Cohn, 2025, needs more optimization.
8 917 0.707013838812 Henry Cohn, 2025, needs more optimization.
8 918 0.707186141715 Henry Cohn, 2026, needs more optimization.
8 919 0.707190386128 Henry Cohn, 2025, needs more optimization.
8 920 0.707192636288 Henry Cohn, 2025, needs more optimization.
8 921 0.707670415856 Henry Cohn, 2025, needs more optimization.
8 923 0.707676716516 Henry Cohn, 2025, needs more optimization.
8 925 0.707694037021 Henry Cohn, 2025, needs more optimization.
8 926 0.707707856101 Henry Cohn, 2025, needs more optimization.
8 928 0.707991000305 Henry Cohn, 2025, needs more optimization.
8 930 0.707996589845 Henry Cohn, 2025, needs more optimization.
8 931 0.708062645930 Henry Cohn, 2025, needs more optimization.
8 932 0.708150395923 Henry Cohn, 2026, needs more optimization.
8 933 0.708152389831 Henry Cohn, 2025, needs more optimization.
8 934 0.708470511601 Henry Cohn, 2026, needs more optimization.
8 935 0.708475101327 Henry Cohn, 2025, needs more optimization.
8 936 0.708482055285 Henry Cohn, 2026, needs more optimization.
8 937 0.708608860965 Henry Cohn, 2025, needs more optimization.
8 938 0.708946530234 Henry Cohn, 2026, needs more optimization.
8 939 0.708951251854 Henry Cohn, 2026, needs more optimization.
8 941 0.708963902315 Henry Cohn, 2025, needs more optimization.
8 942 0.708966792925 Henry Cohn, 2026, needs more optimization.
8 943 0.709002441249 Henry Cohn, 2026, needs more optimization.
8 944 0.709064950292 Henry Cohn, 2025, needs more optimization.
8 946 0.709192766988 Henry Cohn, 2026, needs more optimization.
8 947 0.709257078933 Henry Cohn, 2025, needs more optimization.
8 949 0.709561805584 Henry Cohn, 2025, needs more optimization.
8 950 0.709568370738 Henry Cohn, 2025, needs more optimization.
8 952 0.709580083659 Henry Cohn, 2025, needs more optimization.
8 953 0.709592878533 Henry Cohn, 2026, needs more optimization.
8 954 0.709618223393 Henry Cohn, 2026, needs more optimization.
8 955 0.710013127623 Henry Cohn, 2025, needs more optimization.
8 956 0.710025120237 Henry Cohn, 2025, needs more optimization.
8 957 0.710043299869 Henry Cohn, 2026, needs more optimization.
8 958 0.710045768660 Henry Cohn, 2026, needs more optimization.
8 960 0.710351161619 Henry Cohn, 2026, needs more optimization.
8 961 0.710358683147 Henry Cohn, 2026, needs more optimization.
8 962 0.710752798997 Henry Cohn, 2026, needs more optimization.
8 963 0.710768583393 Henry Cohn, 2026, needs more optimization.
8 964 0.710786430671 Henry Cohn, 2026, needs more optimization.
8 967 0.710794195804 Henry Cohn, 2025, needs more optimization.
8 968 0.710800955289 Henry Cohn, 2025, needs more optimization.
8 969 0.710847532911 Henry Cohn, 2025, needs more optimization.
8 970 0.710949866180 Henry Cohn, 2025, needs more optimization.
8 971 0.711447595345 Henry Cohn, 2026, needs more optimization.
8 972 0.711498673462 Henry Cohn, 2026, needs more optimization.
8 973 0.711510485535 Henry Cohn, 2026, needs more optimization.
8 974 0.711571576014 Henry Cohn, 2025, needs more optimization.
8 975 0.711583352192 Henry Cohn, 2026, needs more optimization.
8 976 0.711588575557 Henry Cohn, 2026, needs more optimization.
8 977 0.711611710434 Henry Cohn, 2025, needs more optimization.
8 978 0.711671964312 Henry Cohn, 2026, needs more optimization.
8 979 0.711962486346 Henry Cohn, 2025, needs more optimization.
8 980 0.711968317112 Henry Cohn, 2026, needs more optimization.
8 981 0.712057436736 Henry Cohn, 2025, needs more optimization.
8 983 0.712080270091 Henry Cohn, 2025, needs more optimization.
8 984 0.712092572803 Henry Cohn, 2026, needs more optimization.
8 986 0.712394668618 Henry Cohn, 2025, needs more optimization.
8 987 0.712408844609 Henry Cohn, 2025, needs more optimization.
8 988 0.712468855396 Henry Cohn, 2026, needs more optimization.
8 989 0.712714678610 Henry Cohn, 2025, needs more optimization.
8 990 0.713101116160 Henry Cohn, 2026, needs more optimization.
8 991 0.713103386410 Henry Cohn, 2025, needs more optimization.
8 992 0.713104668986 Henry Cohn, 2025, needs more optimization.
8 995 0.713130158410 Henry Cohn, 2025, needs more optimization.
8 996 0.713140398164 Henry Cohn, 2025, needs more optimization.
8 1024 0.714285714286 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
7⁢x−5
9 19 0.079067151218 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
441⁢x3−81⁢x2−9⁢x+1
9 20 0.087067958322 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
63⁢x2+6⁢x−1
9 21 0.087067958322 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
63⁢x2+6⁢x−1
9 22 0.109015375240 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
662⁢x4+23⁢x3−67⁢x2−3⁢x+1
9 23 0.114272369686 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
9 24 0.127138702332 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9 25 0.135451570712 H. Cohn, Small spherical and projective codes, data set, updated 2023, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9 26 0.146662063556 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9 27 0.149913487586 H. Cohn, Small spherical and projective codes, data set, updated 2025, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9 28 0.150185176423 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9 29 0.150221104823 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
31⁢x2+2⁢x−1
9 30 0.150221104823 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
31⁢x2+2⁢x−1
9 31 0.150221104823 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
31⁢x2+2⁢x−1
9 32 0.150221104823 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
31⁢x2+2⁢x−1
9 33 0.180525091271 Henry Cohn, 2023.
9 34 0.183408724272 Henry Cohn, 2023.
9 35 0.195176120873 Henry Cohn, 2024.
9 36 0.2 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
5⁢x−1
9 37 0.213781170696 Henry Cohn, 2025.
9 38 0.217703240659 Henry Cohn, 2025.
9 39 0.222837046412 Henry Cohn, 2023.
9 40 0.225659998291 Henry Cohn, 2025.
9 42 0.226907255686 Henry Cohn, 2025.
190336⁢x6+377632⁢x5−322153⁢x4−82188⁢x3+48762⁢x2−972⁢x−729
9 43 0.231201190091 Henry Cohn, 2023.
9 44 0.233554527157 Henry Cohn, 2025.
Minimal polynomial listed in plain text data
9 47 0.238172399483 Henry Cohn, 2023.
335⁢x2−42⁢x−9
9 48 0.254741665820 Henry Cohn, 2025.
9 50 0.256477368938 Henry Cohn, 2026.
23⁢x2−2⁢x−1
9 51 0.266202150382 Henry Cohn, 2025.
9 52 0.267191024627 Henry Cohn, 2023.
71⁢x2−4⁢x−4
9 53 0.269834758170 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
9 54 0.271671378177 Henry Cohn, 2025.
9 56 0.272133267170 Henry Cohn, 2025.
9 57 0.282916244589 Henry Cohn, 2026.
9 58 0.288070633971 Henry Cohn, 2026.
9 59 0.293943006572 Henry Cohn, 2025.
9 60 0.294882506582 Henry Cohn, 2026.
9 61 0.297700422270 Henry Cohn, 2023.
9 62 0.299407593895 Henry Cohn, 2026.
9 63 0.302685227391 Henry Cohn, 2025.
9 64 0.306653313780 Henry Cohn, 2023.
9 65 0.310476186338 Henry Cohn, 2026, needs more optimization.
9 66 0.314219501967 Henry Cohn, 2024.
9 67 0.319305112920 Henry Cohn, 2025.
9 68 0.322050465427 Henry Cohn, 2025.
9 69 0.324666182383 Henry Cohn, 2025.
9 70 0.328147252748 Henry Cohn, 2026, needs more optimization.
9 71 0.329783133617 Henry Cohn, 2026.
9 72 0.330036093460 Henry Cohn, 2025, needs more optimization.
9 73 0.330041808451 Henry Cohn, 2025, needs more optimization.
9 74 0.330099461319 Henry Cohn, 2026, needs more optimization.
9 75 0.330101783843 Henry Cohn, 2025, needs more optimization.
9 78 0.330101895521 Henry Cohn, 2025.
9 79 0.330918543665 Henry Cohn, 2024.
9 80 0.332977706545 Henry Cohn, 2025.
9 96 0.333333333334 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
3⁢x−1
9 97 0.371099110252 Henry Cohn, 2024.
9 98 0.372095101498 Henry Cohn, 2025.
9 101 0.375074698542 Henry Cohn, 2025.
3191⁢x4+68⁢x3−350⁢x2−44⁢x−1
9 102 0.378530782312 Henry Cohn, 2026, needs more optimization.
9 103 0.378850283307 Henry Cohn, 2026, needs more optimization.
9 104 0.379137241782 Henry Cohn, 2025, needs more optimization.
9 105 0.391682453674 Henry Cohn, 2026, needs more optimization.
9 106 0.395189700208 Henry Cohn, 2026, needs more optimization.
9 107 0.398154357334 Henry Cohn, 2026, needs more optimization.
9 108 0.400036672753 Henry Cohn, 2026, needs more optimization.
9 109 0.403046937070 Henry Cohn, 2026, needs more optimization.
9 110 0.405589538580 Henry Cohn, 2026, needs more optimization.
9 111 0.407513805241 Henry Cohn, 2026, needs more optimization.
9 112 0.408810852793 Henry Cohn, 2026, needs more optimization.
9 113 0.411622580981 Henry Cohn, 2026, needs more optimization.
9 114 0.413335694595 Henry Cohn, 2026, needs more optimization.
9 115 0.413676808831 Henry Cohn, 2026, needs more optimization.
9 116 0.414974186672 Henry Cohn, 2026, needs more optimization.
9 117 0.415244094939 Henry Cohn, 2026, needs more optimization.
9 118 0.416652572179 Henry Cohn, 2026, needs more optimization.
9 119 0.417729288063 Henry Cohn, 2026, needs more optimization.
9 120 0.418016338583 Henry Cohn, 2026, needs more optimization.
9 121 0.418798416161 Henry Cohn, 2026, needs more optimization.
9 122 0.420162951570 Henry Cohn, 2026, needs more optimization.
9 123 0.421688820130 Henry Cohn, 2026, needs more optimization.
9 124 0.422247974303 Henry Cohn, 2026, needs more optimization.
9 125 0.422395353957 Henry Cohn, 2026, needs more optimization.
9 126 0.423548828341 Henry Cohn, 2026, needs more optimization.
9 127 0.424952701197 Henry Cohn, 2026, needs more optimization.
9 128 0.426696464552 Henry Cohn, 2026, needs more optimization.
9 129 0.428279428430 Henry Cohn, 2026, needs more optimization.
9 130 0.428571428572 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−3
9 146 0.428571428572 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
7⁢x−3
9 147 0.441717675398 Henry Cohn, 2026, needs more optimization.
9 148 0.444897053449 Henry Cohn, 2026, needs more optimization.
9 149 0.448505735205 Henry Cohn, 2026, needs more optimization.
9 150 0.450668005681 Henry Cohn, 2026, needs more optimization.
9 151 0.452133939640 Henry Cohn, 2026, needs more optimization.
9 152 0.453425179239 Henry Cohn, 2026, needs more optimization.
9 165 0.454545454546 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11⁢x−5
9 166 0.463049784257 Henry Cohn, 2026, needs more optimization.
9 167 0.463421213864 Henry Cohn, 2026, needs more optimization.
9 168 0.464460466840 Henry Cohn, 2026, needs more optimization.
9 169 0.469851035079 Henry Cohn, 2026, needs more optimization.
9 170 0.470339440342 Henry Cohn, 2026, needs more optimization.
9 171 0.471015417577 Henry Cohn, 2026, needs more optimization.
9 172 0.471882837973 Henry Cohn, 2026, needs more optimization.
9 173 0.472631090365 Henry Cohn, 2026, needs more optimization.
9 174 0.473604016858 Henry Cohn, 2026, needs more optimization.
9 175 0.473899443814 Henry Cohn, 2026, needs more optimization.
9 176 0.474154489810 Henry Cohn, 2026, needs more optimization.
9 177 0.474690676718 Henry Cohn, 2026, needs more optimization.
9 178 0.475611201967 Henry Cohn, 2026, needs more optimization.
9 179 0.475623515575 Henry Cohn, 2026, needs more optimization.
9 180 0.476131499428 Henry Cohn, 2026, needs more optimization.
9 181 0.476974776235 Henry Cohn, 2026, needs more optimization.
9 182 0.476976861362 Henry Cohn, 2026, needs more optimization.
9 183 0.477142319793 Henry Cohn, 2026, needs more optimization.
9 185 0.477665845002 Henry Cohn, 2026, needs more optimization.
9 186 0.479219877528 Henry Cohn, 2026, needs more optimization.
9 187 0.479532573313 Henry Cohn, 2026, needs more optimization.
9 188 0.479889494428 Henry Cohn, 2026, needs more optimization.
9 189 0.480321672624 Henry Cohn, 2026, needs more optimization.
9 190 0.480514791926 Henry Cohn, 2025, needs more optimization.
9 191 0.481423660967 Henry Cohn, 2025, needs more optimization.
9 192 0.481706171835 Henry Cohn, 2026, needs more optimization.
9 193 0.482676130493 Henry Cohn, 2026, needs more optimization.
9 194 0.483686161785 Henry Cohn, 2026, needs more optimization.
9 195 0.484721410010 Henry Cohn, 2026, needs more optimization.
9 196 0.484960159278 Henry Cohn, 2026, needs more optimization.
9 197 0.485125511701 Henry Cohn, 2026, needs more optimization.
9 198 0.486164425291 Henry Cohn, 2026, needs more optimization.
9 199 0.486334754136 Henry Cohn, 2026, needs more optimization.
9 200 0.486637780776 Henry Cohn, 2026, needs more optimization.
9 201 0.486923552060 Henry Cohn, 2026, needs more optimization.
9 202 0.487542459477 Henry Cohn, 2026, needs more optimization.
9 203 0.487888050195 Henry Cohn, 2026, needs more optimization.
9 204 0.488717800450 Henry Cohn, 2026, needs more optimization.
9 205 0.489800010772 Henry Cohn, 2026, needs more optimization.
9 206 0.489958130382 Henry Cohn, 2026, needs more optimization.
9 207 0.490280805285 Henry Cohn, 2026, needs more optimization.
9 209 0.490900426266 Henry Cohn, 2026, needs more optimization.
9 210 0.491506550772 Henry Cohn, 2026, needs more optimization.
9 211 0.492180411390 Henry Cohn, 2026, needs more optimization.
9 212 0.493509459815 Henry Cohn, 2026, needs more optimization.
9 213 0.494056228007 Henry Cohn, 2026, needs more optimization.
9 214 0.495420075988 Henry Cohn, 2026, needs more optimization.
9 215 0.495678049387 Henry Cohn, 2026, needs more optimization.
9 216 0.496004138459 Henry Cohn, 2026, needs more optimization.
9 217 0.496427496204 Henry Cohn, 2026, needs more optimization.
9 219 0.496903654512 Henry Cohn, 2026, needs more optimization.
9 220 0.497419918934 Henry Cohn, 2026, needs more optimization.
9 221 0.498899445428 Henry Cohn, 2026, needs more optimization.
9 222 0.498911623597 Henry Cohn, 2026, needs more optimization.
9 223 0.499436655922 Henry Cohn, 2026, needs more optimization.
9 226 0.499490926221 Henry Cohn, 2026, needs more optimization.
9 227 0.499565847311 Henry Cohn, 2026, needs more optimization.
9 230 0.499873727620 Henry Cohn, 2026, needs more optimization.
9 233 0.499931516232 Henry Cohn, 2026, needs more optimization.
9 236 0.499981673823 Henry Cohn, 2026, needs more optimization.
9 306 0.5 J. Leech and N. J. A. Sloane, Sphere packings and error-correcting codes, Canadian J. Math. 23 (1971), 718–745, doi:10.4153/CJM-1971-081-3; H. Cohn and I. Rajagopal, Variations on five-dimensional sphere packings, preprint, 2024, arXiv:2412.00937.
2⁢x−1
9 307 0.517341896236 Henry Cohn, 2024, needs more optimization.
9 308 0.523809525477 Henry Cohn, 2026, needs more optimization.
9 309 0.528129183932 Henry Cohn, 2026, needs more optimization.
9 310 0.536081315987 Henry Cohn, 2026, needs more optimization.
9 311 0.536081422599 Henry Cohn, 2025, needs more optimization.
9 312 0.536116067832 Henry Cohn, 2026, needs more optimization.
9 314 0.536129423307 Henry Cohn, 2025, needs more optimization.
9 316 0.536754266934 Henry Cohn, 2025, needs more optimization.
9 317 0.536763015062 Henry Cohn, 2025, needs more optimization.
9 319 0.536799577609 Henry Cohn, 2025, needs more optimization.
9 320 0.536802180194 Henry Cohn, 2026, needs more optimization.
9 324 0.536804014874 Henry Cohn, 2026, needs more optimization.
9 328 0.536825498604 Henry Cohn, 2026, needs more optimization.
9 332 0.536838164256 Henry Cohn, 2026, needs more optimization.
9 333 0.537239953366 Henry Cohn, 2026, needs more optimization.
9 334 0.537943633154 Henry Cohn, 2025, needs more optimization.
9 335 0.537980963423 Henry Cohn, 2026, needs more optimization.
9 336 0.539493189916 Henry Cohn, 2026, needs more optimization.
9 337 0.540140136178 Henry Cohn, 2025, needs more optimization.
9 338 0.541254001703 Henry Cohn, 2025, needs more optimization.
9 340 0.543183013517 Henry Cohn, 2026, needs more optimization.
9 341 0.544090835364 Henry Cohn, 2026, needs more optimization.
9 482 0.546918160679 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x2−2⁢x−1
9 610 0.6 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−3
9 612 0.6 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
5⁢x−3
9 613 0.614174874984 Henry Cohn, 2025, needs more optimization.
9 614 0.614786340484 Henry Cohn, 2025, needs more optimization.
9 615 0.614905078465 Henry Cohn, 2025, needs more optimization.
9 616 0.615168409892 Henry Cohn, 2026, needs more optimization.
9 617 0.616077792127 Henry Cohn, 2025, needs more optimization.
9 618 0.616092533017 Henry Cohn, 2025, needs more optimization.
9 619 0.616436132892 Henry Cohn, 2025, needs more optimization.
9 636 0.618033985078 Henry Cohn, 2026, needs more optimization.
9 640 0.618033987180 Henry Cohn, 2026, needs more optimization.
9 722 0.618033988750 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
x2+x−1
9 723 0.642621614971 Henry Cohn, 2025, needs more optimization.
9 724 0.642759824040 Henry Cohn, 2026, needs more optimization.
9 725 0.642942346565 Henry Cohn, 2025, needs more optimization.
9 726 0.643197872157 Henry Cohn, 2025, needs more optimization.
9 727 0.643264138767 Henry Cohn, 2025, needs more optimization.
9 728 0.643367753818 Henry Cohn, 2025, needs more optimization.
9 729 0.643669813440 Henry Cohn, 2025, needs more optimization.
9 730 0.643679183146 Henry Cohn, 2026, needs more optimization.
9 731 0.643709726592 Henry Cohn, 2025, needs more optimization.
9 732 0.643712370360 Henry Cohn, 2026, needs more optimization.
9 733 0.643833843770 Henry Cohn, 2025, needs more optimization.
9 734 0.644273059340 Henry Cohn, 2026, needs more optimization.
9 735 0.644276242524 Henry Cohn, 2025, needs more optimization.
9 736 0.644496407810 Henry Cohn, 2025, needs more optimization.
9 737 0.644577686472 Henry Cohn, 2025, needs more optimization.
9 738 0.644591860201 Henry Cohn, 2025, needs more optimization.
9 739 0.644986723180 Henry Cohn, 2025, needs more optimization.
9 740 0.645107975569 Henry Cohn, 2025, needs more optimization.
9 741 0.645116699616 Henry Cohn, 2025, needs more optimization.
9 742 0.645214426924 Henry Cohn, 2025, needs more optimization.
9 743 0.645220929540 Henry Cohn, 2025, needs more optimization.
9 744 0.645358015488 Henry Cohn, 2026, needs more optimization.
9 745 0.645661683498 Henry Cohn, 2025, needs more optimization.
9 746 0.645662904024 Henry Cohn, 2026, needs more optimization.
9 747 0.645677484301 Henry Cohn, 2025, needs more optimization.
9 748 0.645733908744 Henry Cohn, 2026, needs more optimization.
9 749 0.645793318913 Henry Cohn, 2025, needs more optimization.
9 750 0.646059931101 Henry Cohn, 2026, needs more optimization.
9 751 0.646119592607 Henry Cohn, 2025, needs more optimization.
9 752 0.646447386259 Henry Cohn, 2025, needs more optimization.
9 753 0.646636838574 Henry Cohn, 2025, needs more optimization.
9 754 0.646640495508 Henry Cohn, 2026, needs more optimization.
9 755 0.646654817535 Henry Cohn, 2025, needs more optimization.
9 756 0.646809620524 Henry Cohn, 2026, needs more optimization.
9 757 0.647021021451 Henry Cohn, 2025, needs more optimization.
9 758 0.647188302956 Henry Cohn, 2026, needs more optimization.
9 760 0.647415975407 Henry Cohn, 2025, needs more optimization.
9 761 0.647455380135 Henry Cohn, 2025, needs more optimization.
9 762 0.647502273069 Henry Cohn, 2026, needs more optimization.
9 763 0.647890382897 Henry Cohn, 2025, needs more optimization.
9 764 0.647911180488 Henry Cohn, 2026, needs more optimization.
9 765 0.648153662294 Henry Cohn, 2025, needs more optimization.
9 766 0.648179398056 Henry Cohn, 2025, needs more optimization.
9 767 0.648205669668 Henry Cohn, 2025, needs more optimization.
9 768 0.648276344216 Henry Cohn, 2026, needs more optimization.
9 769 0.648498850472 Henry Cohn, 2025, needs more optimization.
9 770 0.648525378931 Henry Cohn, 2026, needs more optimization.
9 771 0.648980224016 Henry Cohn, 2025, needs more optimization.
9 772 0.648988014765 Henry Cohn, 2025, needs more optimization.
9 773 0.649001453595 Henry Cohn, 2025, needs more optimization.
9 774 0.649049866559 Henry Cohn, 2026, needs more optimization.
9 776 0.649337034538 Henry Cohn, 2026, needs more optimization.
9 777 0.649384395508 Henry Cohn, 2025, needs more optimization.
9 778 0.649386637141 Henry Cohn, 2025, needs more optimization.
9 779 0.649893766152 Henry Cohn, 2025, needs more optimization.
9 780 0.649924079901 Henry Cohn, 2025, needs more optimization.
9 781 0.649983318032 Henry Cohn, 2025, needs more optimization.
9 782 0.650115707659 Henry Cohn, 2025, needs more optimization.
9 783 0.650132298446 Henry Cohn, 2025, needs more optimization.
9 784 0.650177798115 Henry Cohn, 2026, needs more optimization.
9 785 0.650209071935 Henry Cohn, 2025, needs more optimization.
9 786 0.650691249426 Henry Cohn, 2026, needs more optimization.
9 787 0.650727478554 Henry Cohn, 2025, needs more optimization.
9 788 0.650760346949 Henry Cohn, 2026, needs more optimization.
9 789 0.650845223621 Henry Cohn, 2025, needs more optimization.
9 790 0.651076572262 Henry Cohn, 2026, needs more optimization.
9 791 0.651297099799 Henry Cohn, 2025, needs more optimization.
9 792 0.651301357390 Henry Cohn, 2025, needs more optimization.
9 793 0.651428922736 Henry Cohn, 2025, needs more optimization.
9 794 0.651526523791 Henry Cohn, 2026, needs more optimization.
9 795 0.651650729064 Henry Cohn, 2025, needs more optimization.
9 796 0.651657860374 Henry Cohn, 2025, needs more optimization.
9 797 0.651683050917 Henry Cohn, 2025, needs more optimization.
9 798 0.651897804106 Henry Cohn, 2026, needs more optimization.
9 799 0.652152977981 Henry Cohn, 2025, needs more optimization.
9 800 0.652161370068 Henry Cohn, 2026, needs more optimization.
9 801 0.652216667734 Henry Cohn, 2025, needs more optimization.
9 802 0.652274223271 Henry Cohn, 2026, needs more optimization.
9 803 0.652517319296 Henry Cohn, 2025, needs more optimization.
9 804 0.652549189881 Henry Cohn, 2026, needs more optimization.
9 805 0.652558339614 Henry Cohn, 2025, needs more optimization.
9 806 0.652702137773 Henry Cohn, 2026, needs more optimization.
9 807 0.652908801011 Henry Cohn, 2025, needs more optimization.
9 808 0.652955833314 Henry Cohn, 2026, needs more optimization.
9 809 0.653154055619 Henry Cohn, 2025, needs more optimization.
9 810 0.653167528053 Henry Cohn, 2026, needs more optimization.
9 811 0.653237964994 Henry Cohn, 2025, needs more optimization.
9 812 0.653369918581 Henry Cohn, 2025, needs more optimization.
9 813 0.653468008252 Henry Cohn, 2025, needs more optimization.
9 814 0.653677664001 Henry Cohn, 2026, needs more optimization.
9 815 0.653810905202 Henry Cohn, 2025, needs more optimization.
9 816 0.653818231082 Henry Cohn, 2025, needs more optimization.
9 817 0.653850602560 Henry Cohn, 2025, needs more optimization.
9 818 0.653919993720 Henry Cohn, 2026, needs more optimization.
9 819 0.654183709186 Henry Cohn, 2025, needs more optimization.
9 820 0.654189110499 Henry Cohn, 2026, needs more optimization.
9 821 0.654222384679 Henry Cohn, 2025, needs more optimization.
9 822 0.654258849453 Henry Cohn, 2025, needs more optimization.
9 823 0.654391315013 Henry Cohn, 2025, needs more optimization.
9 824 0.654468550447 Henry Cohn, 2025, needs more optimization.
9 825 0.654615045723 Henry Cohn, 2025, needs more optimization.
9 826 0.654819846122 Henry Cohn, 2026, needs more optimization.
9 827 0.655001601010 Henry Cohn, 2025, needs more optimization.
9 828 0.655004842296 Henry Cohn, 2025, needs more optimization.
9 829 0.655220733720 Henry Cohn, 2025, needs more optimization.
9 830 0.655442763615 Henry Cohn, 2025, needs more optimization.
9 831 0.655452949080 Henry Cohn, 2025, needs more optimization.
9 832 0.655463034710 Henry Cohn, 2026, needs more optimization.
9 833 0.655679432859 Henry Cohn, 2025, needs more optimization.
9 834 0.655681418143 Henry Cohn, 2026, needs more optimization.
9 835 0.655845468606 Henry Cohn, 2025, needs more optimization.
9 836 0.655868714138 Henry Cohn, 2026, needs more optimization.
9 837 0.656262456101 Henry Cohn, 2025, needs more optimization.
9 838 0.656288861246 Henry Cohn, 2026, needs more optimization.
9 839 0.656381129178 Henry Cohn, 2025, needs more optimization.
9 840 0.656565559996 Henry Cohn, 2025, needs more optimization.
9 842 0.656810400690 Henry Cohn, 2026, needs more optimization.
9 843 0.657094679486 Henry Cohn, 2025, needs more optimization.
9 844 0.657098253250 Henry Cohn, 2025, needs more optimization.
9 845 0.657208605166 Henry Cohn, 2025, needs more optimization.
9 846 0.657393872630 Henry Cohn, 2025, needs more optimization.
9 847 0.657415668854 Henry Cohn, 2025, needs more optimization.
9 848 0.657418448672 Henry Cohn, 2025, needs more optimization.
9 849 0.657451067624 Henry Cohn, 2025, needs more optimization.
9 850 0.657531881331 Henry Cohn, 2025, needs more optimization.
9 851 0.657751538905 Henry Cohn, 2025, needs more optimization.
9 852 0.657805663087 Henry Cohn, 2026, needs more optimization.
9 853 0.657807774320 Henry Cohn, 2025, needs more optimization.
9 854 0.657813045189 Henry Cohn, 2026, needs more optimization.
9 855 0.658005911534 Henry Cohn, 2025, needs more optimization.
9 856 0.658328451121 Henry Cohn, 2025, needs more optimization.
9 857 0.658392377535 Henry Cohn, 2025, needs more optimization.
9 858 0.658604634171 Henry Cohn, 2026, needs more optimization.
9 859 0.658612838651 Henry Cohn, 2025, needs more optimization.
9 860 0.658835820210 Henry Cohn, 2026, needs more optimization.
9 861 0.658839041199 Henry Cohn, 2025, needs more optimization.
9 862 0.659031437873 Henry Cohn, 2025, needs more optimization.
9 863 0.659046632503 Henry Cohn, 2025, needs more optimization.
9 864 0.659261179677 Henry Cohn, 2025, needs more optimization.
9 865 0.659346409902 Henry Cohn, 2025, needs more optimization.
9 866 0.659356134011 Henry Cohn, 2025, needs more optimization.
9 867 0.659595134719 Henry Cohn, 2025, needs more optimization.
9 868 0.659605999850 Henry Cohn, 2025, needs more optimization.
9 869 0.659633383665 Henry Cohn, 2025, needs more optimization.
9 870 0.659782748322 Henry Cohn, 2026, needs more optimization.
9 871 0.659790551741 Henry Cohn, 2025, needs more optimization.
9 872 0.660017704676 Henry Cohn, 2026, needs more optimization.
9 873 0.660131662979 Henry Cohn, 2025, needs more optimization.
9 874 0.660230563294 Henry Cohn, 2026, needs more optimization.
9 875 0.660493680174 Henry Cohn, 2025, needs more optimization.
9 876 0.660497979113 Henry Cohn, 2026, needs more optimization.
9 877 0.660503958980 Henry Cohn, 2025, needs more optimization.
9 878 0.660528229665 Henry Cohn, 2026, needs more optimization.
9 879 0.660588079957 Henry Cohn, 2025, needs more optimization.
9 880 0.660632906756 Henry Cohn, 2026, needs more optimization.
9 881 0.660977908488 Henry Cohn, 2025, needs more optimization.
9 882 0.661023469661 Henry Cohn, 2026, needs more optimization.
9 883 0.661040763292 Henry Cohn, 2025, needs more optimization.
9 884 0.661155559221 Henry Cohn, 2026, needs more optimization.
9 885 0.661241996052 Henry Cohn, 2025, needs more optimization.
9 886 0.661245073071 Henry Cohn, 2025, needs more optimization.
9 887 0.661291585997 Henry Cohn, 2025, needs more optimization.
9 888 0.661647282768 Henry Cohn, 2026, needs more optimization.
9 889 0.661698386742 Henry Cohn, 2025, needs more optimization.
9 890 0.661734238751 Henry Cohn, 2026, needs more optimization.
9 891 0.661744741460 Henry Cohn, 2025, needs more optimization.
9 892 0.661934946059 Henry Cohn, 2026, needs more optimization.
9 893 0.661993639527 Henry Cohn, 2025, needs more optimization.
9 894 0.662032980058 Henry Cohn, 2026, needs more optimization.
9 895 0.662247016230 Henry Cohn, 2025, needs more optimization.
9 896 0.662283643031 Henry Cohn, 2026, needs more optimization.
9 897 0.662309931828 Henry Cohn, 2025, needs more optimization.
9 898 0.662524539542 Henry Cohn, 2026, needs more optimization.
9 899 0.662537919598 Henry Cohn, 2025, needs more optimization.
9 900 0.662636126846 Henry Cohn, 2025, needs more optimization.
9 901 0.662642382986 Henry Cohn, 2025, needs more optimization.
9 902 0.663087337091 Henry Cohn, 2026, needs more optimization.
9 903 0.663138901634 Henry Cohn, 2025, needs more optimization.
9 904 0.663151783688 Henry Cohn, 2025, needs more optimization.
9 905 0.663186631313 Henry Cohn, 2025, needs more optimization.
9 906 0.663321732544 Henry Cohn, 2025, needs more optimization.
9 907 0.663376500633 Henry Cohn, 2025, needs more optimization.
9 908 0.663412535064 Henry Cohn, 2026, needs more optimization.
9 909 0.663585246596 Henry Cohn, 2025, needs more optimization.
9 910 0.663640087295 Henry Cohn, 2026, needs more optimization.
9 911 0.663880945005 Henry Cohn, 2025, needs more optimization.
9 912 0.663891728453 Henry Cohn, 2026, needs more optimization.
9 913 0.663893472277 Henry Cohn, 2025, needs more optimization.
9 914 0.663907227269 Henry Cohn, 2026, needs more optimization.
9 915 0.664027862761 Henry Cohn, 2025, needs more optimization.
9 916 0.664221329263 Henry Cohn, 2026, needs more optimization.
9 917 0.664228513191 Henry Cohn, 2025, needs more optimization.
9 918 0.664316325074 Henry Cohn, 2026, needs more optimization.
9 919 0.664694543885 Henry Cohn, 2025, needs more optimization.
9 920 0.664707746199 Henry Cohn, 2026, needs more optimization.
9 921 0.664729861899 Henry Cohn, 2025, needs more optimization.
9 922 0.665008783421 Henry Cohn, 2025, needs more optimization.
9 923 0.665059203223 Henry Cohn, 2025, needs more optimization.
9 924 0.665085819662 Henry Cohn, 2026, needs more optimization.
9 925 0.665334349699 Henry Cohn, 2025, needs more optimization.
9 926 0.665358156161 Henry Cohn, 2026, needs more optimization.
9 927 0.665376822237 Henry Cohn, 2025, needs more optimization.
9 928 0.665655225021 Henry Cohn, 2025, needs more optimization.
9 929 0.665658867246 Henry Cohn, 2025, needs more optimization.
9 930 0.665736024728 Henry Cohn, 2026, needs more optimization.
9 931 0.666044425708 Henry Cohn, 2025, needs more optimization.
9 1008 0.666666666667 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−2
9 1024 0.666666666667 Subcode of a code of size 1056 from M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
3⁢x−2
10 21 0.072033139843 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
640⁢x3−100⁢x2−10⁢x+1
10 22 0.083956154719 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10 23 0.086853938956 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10 24 0.098710133500 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
613376⁢x8−228096⁢x7+40432⁢x6+16416⁢x5−8016⁢x4−216⁢x3+184⁢x2−1
10 25 0.104476374556 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10 26 0.104477652124 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10 27 0.124212414191 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10 28 0.128238684469 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
92⁢x2−4⁢x−1
10 29 0.130634295944 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
10 30 0.138418790027 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10 31 0.144114939804 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
10 32 0.146959243017 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
279⁢x4−420⁢x3+102⁢x2−1
10 33 0.150071241046 Henry Cohn, 2025.
10 34 0.150182198338 Henry Cohn, 2025.
10 35 0.157397110567 Henry Cohn, 2025.
10 36 0.164041833761 Henry Cohn, 2023.
10 40 0.166666666667 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
6⁢x−1
10 41 0.176776695297 Henry Cohn, 2023.
32⁢x2−1
10 42 0.196163849637 Henry Cohn, 2026.
10 43 0.205622503031 Henry Cohn, 2025.
10 44 0.210550138817 Henry Cohn, 2025.
10 45 0.210753585520 Henry Cohn, 2025.
10 46 0.210850169054 Henry Cohn, 2025.
10 50 0.210852996458 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
71⁢x2+4⁢x−4
10 51 0.216689708737 Henry Cohn, 2025.
10 57 0.231237647788 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
36⁢x2−4⁢x−1
10 58 0.25 Henry Cohn, 2024.
4⁢x−1
10 59 0.253695768464 Henry Cohn, 2024.
10 60 0.254730982571 Henry Cohn, 2026.
10 63 0.257944905339 Henry Cohn, 2025.
10 64 0.260558294031 Henry Cohn, 2026, needs more optimization.
10 65 0.264885834877 Henry Cohn, 2025.
10 66 0.265168946762 Henry Cohn, 2025.
10 67 0.268064425530 Henry Cohn, 2025.
10 68 0.269390887696 Henry Cohn, 2026, needs more optimization.
10 69 0.269775337251 Henry Cohn, 2026, needs more optimization.
10 70 0.271729029649 Henry Cohn, 2026, needs more optimization.
10 71 0.272033522200 Henry Cohn, 2026, needs more optimization.
10 72 0.274448309623 Henry Cohn, 2026, needs more optimization.
10 73 0.275987133320 Henry Cohn, 2025.
10 74 0.279604561566 Henry Cohn, 2025.
10 76 0.284096667917 Henry Cohn, 2025.
10 77 0.284910960402 Henry Cohn, 2025.
10 78 0.289897948557 Henry Cohn, 2026.
5⁢x2+2⁢x−1
10 79 0.295299509598 Henry Cohn, 2026, needs more optimization.
10 80 0.299108578097 Henry Cohn, 2026, needs more optimization.
10 81 0.301784416185 Henry Cohn, 2026, needs more optimization.
10 82 0.304464263561 Henry Cohn, 2026, needs more optimization.
10 83 0.308261736865 Henry Cohn, 2026, needs more optimization.
10 84 0.311152230093 Henry Cohn, 2026, needs more optimization.
10 85 0.318255786436 Henry Cohn, 2026, needs more optimization.
10 86 0.322961942252 Henry Cohn, 2026, needs more optimization.
10 87 0.323798687008 Henry Cohn, 2026, needs more optimization.
10 88 0.324407524635 Henry Cohn, 2026, needs more optimization.
10 89 0.324779870327 Henry Cohn, 2026, needs more optimization.
10 90 0.325682059268 Henry Cohn, 2026, needs more optimization.
10 91 0.326611883339 Henry Cohn, 2026, needs more optimization.
10 92 0.328560709595 Henry Cohn, 2026, needs more optimization.
10 93 0.329063708307 Henry Cohn, 2026, needs more optimization.
10 94 0.329784568962 Henry Cohn, 2026, needs more optimization.
10 95 0.329854854198 Henry Cohn, 2025, needs more optimization.
10 96 0.330315697732 Henry Cohn, 2025, needs more optimization.
10 97 0.330625833741 Henry Cohn, 2026, needs more optimization.
10 98 0.330715014152 Henry Cohn, 2026, needs more optimization.
10 99 0.330884838173 Henry Cohn, 2026, needs more optimization.
10 100 0.331093369801 Henry Cohn, 2026, needs more optimization.
10 101 0.331208870453 Henry Cohn, 2026, needs more optimization.
10 102 0.331404605258 Henry Cohn, 2026, needs more optimization.
10 103 0.333258404202 Henry Cohn, 2025, needs more optimization.
10 104 0.333261975589 Henry Cohn, 2025, needs more optimization.
10 105 0.333276446551 Henry Cohn, 2025, needs more optimization.
10 107 0.333327625778 Henry Cohn, 2023, needs more optimization.
10 108 0.333329834036 Henry Cohn, 2023, needs more optimization.
10 109 0.335271812065 Henry Cohn, 2026, needs more optimization.
10 110 0.339668071343 Henry Cohn, 2026, needs more optimization.
10 111 0.342369261176 Henry Cohn, 2024, needs more optimization.
10 112 0.347037575649 Henry Cohn, 2023, needs more optimization.
10 113 0.348033914968 Henry Cohn, 2026, needs more optimization.
10 114 0.350518184001 Henry Cohn, 2026, needs more optimization.
10 115 0.352629567807 Henry Cohn, 2023, needs more optimization.
10 116 0.354011173451 Henry Cohn, 2026, needs more optimization.
10 117 0.360200535278 Henry Cohn, 2026, needs more optimization.
10 118 0.362483350895 Henry Cohn, 2026, needs more optimization.
10 119 0.363780366773 Henry Cohn, 2026, needs more optimization.
10 120 0.364675140118 Henry Cohn, 2026, needs more optimization.
10 121 0.365330581483 Henry Cohn, 2026, needs more optimization.
10 122 0.365464158252 Henry Cohn, 2026, needs more optimization.
10 123 0.365550207038 Henry Cohn, 2026, needs more optimization.
10 124 0.365550207044 Henry Cohn, 2026, needs more optimization.
10 125 0.365553853161 Henry Cohn, 2026, needs more optimization.
10 126 0.365563082891 Henry Cohn, 2026, needs more optimization.
10 127 0.366035053027 Henry Cohn, 2024.
10 128 0.367843527953 Henry Cohn, 2026, needs more optimization.
10 129 0.370543052736 Henry Cohn, 2026, needs more optimization.
10 130 0.371247320309 Henry Cohn, 2026, needs more optimization.
10 131 0.371343753631 Henry Cohn, 2026, needs more optimization.
10 132 0.371412003523 Henry Cohn, 2026, needs more optimization.
10 133 0.385291927187 Henry Cohn, 2026, needs more optimization.
10 134 0.390476324117 Henry Cohn, 2026, needs more optimization.
10 135 0.392361953682 Henry Cohn, 2026, needs more optimization.
10 136 0.393476980357 Henry Cohn, 2026, needs more optimization.
10 137 0.396284337244 Henry Cohn, 2026, needs more optimization.
10 138 0.398651390978 Henry Cohn, 2026, needs more optimization.
10 139 0.400282439529 Henry Cohn, 2026, needs more optimization.
10 140 0.401787414255 Henry Cohn, 2026, needs more optimization.
10 141 0.403139490794 Henry Cohn, 2026, needs more optimization.
10 142 0.404397831501 Henry Cohn, 2026, needs more optimization.
10 156 0.405827419558 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11⁢x2−2⁢x−1
10 157 0.414621362629 Henry Cohn, 2026, needs more optimization.
10 158 0.414717098070 Henry Cohn, 2026, needs more optimization.
10 159 0.415368955508 Henry Cohn, 2026, needs more optimization.
10 160 0.416899871465 Henry Cohn, 2026, needs more optimization.
10 161 0.417719534741 Henry Cohn, 2026, needs more optimization.
10 162 0.419439435006 Henry Cohn, 2026, needs more optimization.
10 163 0.419846515862 Henry Cohn, 2026, needs more optimization.
10 164 0.420594116242 Henry Cohn, 2026, needs more optimization.
10 165 0.421680629361 Henry Cohn, 2026, needs more optimization.
10 166 0.422486778390 Henry Cohn, 2026, needs more optimization.
10 167 0.423471709473 Henry Cohn, 2026, needs more optimization.
10 168 0.424392647086 Henry Cohn, 2026, needs more optimization.
10 169 0.425571935807 Henry Cohn, 2026, needs more optimization.
10 170 0.426224622819 Henry Cohn, 2026, needs more optimization.
10 194 0.428571428572 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−3
10 195 0.438794942781 Henry Cohn, 2026, needs more optimization.
10 196 0.441244812778 Henry Cohn, 2026, needs more optimization.
10 197 0.444349112446 Henry Cohn, 2026, needs more optimization.
10 198 0.445616632853 Henry Cohn, 2026, needs more optimization.
10 199 0.447506975720 Henry Cohn, 2026, needs more optimization.
10 200 0.448710506540 Henry Cohn, 2026, needs more optimization.
10 201 0.449839177297 Henry Cohn, 2026, needs more optimization.
10 202 0.451325831296 Henry Cohn, 2026, needs more optimization.
10 203 0.452910144118 Henry Cohn, 2026, needs more optimization.
10 204 0.454050199116 Henry Cohn, 2026, needs more optimization.
10 205 0.455133784432 Henry Cohn, 2026, needs more optimization.
10 206 0.455644447825 Henry Cohn, 2026, needs more optimization.
10 207 0.456441808540 Henry Cohn, 2026, needs more optimization.
10 208 0.457333439092 Henry Cohn, 2026, needs more optimization.
10 209 0.458279786503 Henry Cohn, 2026, needs more optimization.
10 210 0.458964524611 Henry Cohn, 2026, needs more optimization.
10 211 0.460210800072 Henry Cohn, 2026, needs more optimization.
10 212 0.461036660768 Henry Cohn, 2026, needs more optimization.
10 213 0.461546920265 Henry Cohn, 2026, needs more optimization.
10 214 0.462330014777 Henry Cohn, 2026, needs more optimization.
10 215 0.462922219765 Henry Cohn, 2026, needs more optimization.
10 216 0.463437884482 Henry Cohn, 2026, needs more optimization.
10 217 0.464265248726 Henry Cohn, 2026, needs more optimization.
10 218 0.464842221344 Henry Cohn, 2026, needs more optimization.
10 219 0.465617348656 Henry Cohn, 2026, needs more optimization.
10 220 0.466322137803 Henry Cohn, 2026, needs more optimization.
10 221 0.467482112413 Henry Cohn, 2026, needs more optimization.
10 222 0.468061072174 Henry Cohn, 2026, needs more optimization.
10 223 0.468157456685 Henry Cohn, 2026, needs more optimization.
10 224 0.469170170457 Henry Cohn, 2026, needs more optimization.
10 225 0.469584222301 Henry Cohn, 2026, needs more optimization.
10 226 0.470458414305 Henry Cohn, 2026, needs more optimization.
10 227 0.470668002387 Henry Cohn, 2026, needs more optimization.
10 228 0.471513884513 Henry Cohn, 2026, needs more optimization.
10 229 0.472012735283 Henry Cohn, 2026, needs more optimization.
10 230 0.472312694860 Henry Cohn, 2026, needs more optimization.
10 231 0.473038122940 Henry Cohn, 2026, needs more optimization.
10 232 0.473654445513 Henry Cohn, 2026, needs more optimization.
10 233 0.474225192722 Henry Cohn, 2026, needs more optimization.
10 234 0.474856685492 Henry Cohn, 2026, needs more optimization.
10 235 0.475609641310 Henry Cohn, 2026, needs more optimization.
10 236 0.475887735542 Henry Cohn, 2026, needs more optimization.
10 237 0.476614761037 Henry Cohn, 2026, needs more optimization.
10 238 0.476849474029 Henry Cohn, 2026, needs more optimization.
10 239 0.477375802062 Henry Cohn, 2026, needs more optimization.
10 240 0.477989623034 Henry Cohn, 2026, needs more optimization.
10 241 0.478625589992 Henry Cohn, 2026, needs more optimization.
10 242 0.478836680841 Henry Cohn, 2026, needs more optimization.
10 243 0.479804581520 Henry Cohn, 2026, needs more optimization.
10 244 0.480174862321 Henry Cohn, 2025, needs more optimization.
10 245 0.480656799369 Henry Cohn, 2026, needs more optimization.
10 246 0.480823597780 Henry Cohn, 2026, needs more optimization.
10 247 0.481640880417 Henry Cohn, 2026, needs more optimization.
10 248 0.482126232909 Henry Cohn, 2026, needs more optimization.
10 249 0.482343451625 Henry Cohn, 2026, needs more optimization.
10 250 0.483178176586 Henry Cohn, 2026, needs more optimization.
10 251 0.483751253565 Henry Cohn, 2026, needs more optimization.
10 252 0.483930791289 Henry Cohn, 2026, needs more optimization.
10 253 0.484298065498 Henry Cohn, 2026, needs more optimization.
10 254 0.484907365786 Henry Cohn, 2026, needs more optimization.
10 255 0.485447578924 Henry Cohn, 2025, needs more optimization.
10 256 0.485731865466 Henry Cohn, 2026, needs more optimization.
10 257 0.486672423361 Henry Cohn, 2025, needs more optimization.
10 258 0.486776582276 Henry Cohn, 2026, needs more optimization.
10 259 0.487018831175 Henry Cohn, 2026, needs more optimization.
10 260 0.487245498226 Henry Cohn, 2026, needs more optimization.
10 261 0.487929839871 Henry Cohn, 2025, needs more optimization.
10 262 0.488010638917 Henry Cohn, 2026, needs more optimization.
10 263 0.488239068865 Henry Cohn, 2025, needs more optimization.
10 264 0.488516850916 Henry Cohn, 2026, needs more optimization.
10 266 0.489123105197 Henry Cohn, 2026, needs more optimization.
10 267 0.489406647251 Henry Cohn, 2025, needs more optimization.
10 268 0.489432185993 Henry Cohn, 2026, needs more optimization.
10 269 0.489460592787 Henry Cohn, 2026, needs more optimization.
10 270 0.489779664020 Henry Cohn, 2026, needs more optimization.
10 271 0.490498162985 Henry Cohn, 2026, needs more optimization.
10 272 0.491244721518 Henry Cohn, 2025, needs more optimization.
10 273 0.491972289470 Henry Cohn, 2026, needs more optimization.
10 274 0.492815363438 Henry Cohn, 2026, needs more optimization.
10 275 0.492974194470 Henry Cohn, 2025, needs more optimization.
10 276 0.493652933296 Henry Cohn, 2026, needs more optimization.
10 277 0.494231294583 Henry Cohn, 2025, needs more optimization.
10 278 0.494572195718 Henry Cohn, 2025, needs more optimization.
10 279 0.495102468877 Henry Cohn, 2026, needs more optimization.
10 280 0.495331458923 Henry Cohn, 2026, needs more optimization.
10 281 0.495864792167 Henry Cohn, 2026, needs more optimization.
10 282 0.496305591849 Henry Cohn, 2025, needs more optimization.
10 284 0.496801495945 Henry Cohn, 2026, needs more optimization.
10 285 0.497348375179 Henry Cohn, 2026, needs more optimization.
10 286 0.497472935288 Henry Cohn, 2026, needs more optimization.
10 287 0.497733487648 Henry Cohn, 2026, needs more optimization.
10 288 0.498485715924 Henry Cohn, 2026, needs more optimization.
10 289 0.498730653434 Henry Cohn, 2026, needs more optimization.
10 290 0.499127242647 Henry Cohn, 2026, needs more optimization.
10 291 0.499804808742 Henry Cohn, 2026, needs more optimization.
10 500 0.5 J. Leech and N. J. A. Sloane, Sphere packings and error-correcting codes, Canadian J. Math. 23 (1971), 718–745, doi:10.4153/CJM-1971-081-3.
2⁢x−1
10 510 0.5 M. Ganzhinov, Highly symmetric lines, Linear Algebra Appl. 722 (2025), 12–37, doi:10.1016/j.laa.2025.05.002.
2⁢x−1
10 596 0.555555555556 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−5
10 740 0.564577451054 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
92⁢x2−36⁢x−9
10 1024 0.6 Subcode of a code of size 1190 from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−3
11 23 0.066201272532 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
891⁢x3−121⁢x2−11⁢x+1
11 24 0.077294525867 H. Cohn, Small spherical and projective codes, data set, updated 2025, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
11 25 0.083618757829 H. Cohn, Small spherical and projective codes, data set, updated 2023, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
11 26 0.090957106782 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
11 27 0.096579767338 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
11 28 0.102062072616 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
96⁢x2−1
11 29 0.108541175054 H. Cohn, Small spherical and projective codes, data set, updated 2025, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
11 30 0.111111111112 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9⁢x−1
11 31 0.116882716629 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
1880159⁢x4+662980⁢x3+23850⁢x2−9500⁢x−625
11 32 0.127120178791 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
11 33 0.130869404972 Henry Cohn, 2023.
4276703⁢x4+1417464⁢x3−4824⁢x2−23328⁢x−1296
11 35 0.134804262191 Henry Cohn, 2023.
379⁢x2−14⁢x−5
11 36 0.135617659465 Henry Cohn, 2023.
34679⁢x4+11944⁢x3+264⁢x2−224⁢x−16
11 37 0.141119306055 Henry Cohn, 2023.
11 40 0.142857142858 H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
7⁢x−1
11 41 0.151608920662 Henry Cohn, 2023.
215⁢x2−26⁢x−1
11 42 0.152689377129 Henry Cohn, 2023.
441⁢x4+84⁢x3−66⁢x2+1
11 43 0.154540745580 Henry Cohn, 2024.
11 44 0.164387348702 Henry Cohn, 2023.
11 45 0.167764862361 Henry Cohn, 2023.
11 46 0.173024920814 Henry Cohn, 2023.
11 47 0.193275935700 Henry Cohn, 2025.
11 48 0.198565163418 Henry Cohn, 2025.
11 49 0.201215495510 Henry Cohn, 2025.
11 50 0.204931262058 Henry Cohn, 2025.
11 51 0.204957387535 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
11 52 0.208005237402 Henry Cohn, 2024.
11 53 0.209775126698 Henry Cohn, 2026.
11 54 0.210461540583 Henry Cohn, 2026, needs more optimization.
11 55 0.211949051009 Henry Cohn, 2026.
11 56 0.214650086321 Henry Cohn, 2026.
11 61 0.214737233855 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
31⁢x2−2⁢x−1
11 68 0.232764852407 Henry Cohn, 2024.
295⁢x2−30⁢x−9
11 69 0.241565014044 Henry Cohn, 2025.
11 70 0.244726315701 Henry Cohn, 2026.
11 71 0.255919437719 Henry Cohn, 2026, needs more optimization.
11 72 0.256477843138 Henry Cohn, 2026, needs more optimization.
11 73 0.259229428292 Henry Cohn, 2026, needs more optimization.
11 74 0.259520094012 Henry Cohn, 2026, needs more optimization.
11 75 0.259754902333 Henry Cohn, 2026, needs more optimization.
11 76 0.260611782278 Henry Cohn, 2026, needs more optimization.
11 77 0.260659763728 Henry Cohn, 2026, needs more optimization.
11 78 0.260823410840 Henry Cohn, 2026, needs more optimization.
11 79 0.261256577214 Henry Cohn, 2026, needs more optimization.
11 80 0.261313630060 Henry Cohn, 2026, needs more optimization.
11 81 0.262008277852 Henry Cohn, 2026, needs more optimization.
11 82 0.263455971662 Henry Cohn, 2026, needs more optimization.
11 83 0.264198763290 Henry Cohn, 2026, needs more optimization.
11 84 0.265230263115 Henry Cohn, 2026, needs more optimization.
11 85 0.266218308143 Henry Cohn, 2026, needs more optimization.
11 90 0.267191024627 Henry Cohn, 2026.
71⁢x2−4⁢x−4
11 91 0.273036354862 Henry Cohn, 2026, needs more optimization.
11 92 0.280653491593 Henry Cohn, 2026, needs more optimization.
11 93 0.281719231974 Henry Cohn, 2026, needs more optimization.
11 94 0.282962812797 Henry Cohn, 2026, needs more optimization.
11 95 0.283938928367 Henry Cohn, 2026, needs more optimization.
11 96 0.285631420356 Henry Cohn, 2026, needs more optimization.
11 97 0.286255983593 Henry Cohn, 2026, needs more optimization.
11 98 0.287807016130 Henry Cohn, 2026, needs more optimization.
11 99 0.289831202843 Henry Cohn, 2026, needs more optimization.
11 100 0.299916029374 Henry Cohn, 2026, needs more optimization.
11 101 0.302929489511 Henry Cohn, 2026, needs more optimization.
11 102 0.304623603863 Henry Cohn, 2026, needs more optimization.
11 103 0.305756497969 Henry Cohn, 2026, needs more optimization.
11 104 0.306554011452 Henry Cohn, 2026, needs more optimization.
11 105 0.307098305054 Henry Cohn, 2026, needs more optimization.
11 106 0.307737954219 Henry Cohn, 2026, needs more optimization.
11 107 0.310786210625 Henry Cohn, 2026, needs more optimization.
11 108 0.317734326003 Henry Cohn, 2026, needs more optimization.
11 109 0.320412997083 Henry Cohn, 2026, needs more optimization.
11 110 0.321720197391 Henry Cohn, 2026, needs more optimization.
11 111 0.324288501970 Henry Cohn, 2026, needs more optimization.
11 112 0.324893666946 Henry Cohn, 2026, needs more optimization.
11 113 0.325064953334 Henry Cohn, 2026, needs more optimization.
11 114 0.325267916253 Henry Cohn, 2026, needs more optimization.
11 115 0.325412321402 Henry Cohn, 2026, needs more optimization.
11 116 0.325687794553 Henry Cohn, 2026, needs more optimization.
11 117 0.325913410900 Henry Cohn, 2026, needs more optimization.
11 118 0.326109198423 Henry Cohn, 2026, needs more optimization.
11 119 0.326373145257 Henry Cohn, 2026, needs more optimization.
11 120 0.326580746251 Henry Cohn, 2026, needs more optimization.
11 121 0.326847196383 Henry Cohn, 2026, needs more optimization.
11 122 0.327076280459 Henry Cohn, 2026, needs more optimization.
11 123 0.328161428278 Henry Cohn, 2026, needs more optimization.
11 124 0.328656833607 Henry Cohn, 2026, needs more optimization.
11 125 0.332693323364 Henry Cohn, 2026, needs more optimization.
11 126 0.332775966757 Henry Cohn, 2026, needs more optimization.
11 127 0.332908701031 Henry Cohn, 2026, needs more optimization.
11 128 0.333030047873 Henry Cohn, 2026, needs more optimization.
11 129 0.333205495741 Henry Cohn, 2026, needs more optimization.
11 130 0.333276029314 Henry Cohn, 2024, needs more optimization.
11 131 0.333329294372 Henry Cohn, 2026, needs more optimization.
11 132 0.333331284034 Henry Cohn, 2026, needs more optimization.
11 136 0.333333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−1
11 156 0.333333333334 M. Ganzhinov, Highly symmetric lines, Linear Algebra Appl. 722 (2025), 12–37, doi:10.1016/j.laa.2025.05.002.
3⁢x−1
11 157 0.361630937422 Henry Cohn, 2026, needs more optimization.
11 158 0.368903940543 Henry Cohn, 2026, needs more optimization.
11 159 0.369353319945 Henry Cohn, 2026, needs more optimization.
11 160 0.372290513598 Henry Cohn, 2026, needs more optimization.
11 166 0.375 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
8⁢x−3
11 167 0.387129328095 Henry Cohn, 2026, needs more optimization.
11 168 0.389149249357 Henry Cohn, 2026, needs more optimization.
11 169 0.390142039413 Henry Cohn, 2026, needs more optimization.
11 170 0.391461642085 Henry Cohn, 2026, needs more optimization.
11 171 0.392663841405 Henry Cohn, 2026, needs more optimization.
11 172 0.393647384217 Henry Cohn, 2025, needs more optimization.
11 173 0.395017527530 Henry Cohn, 2025, needs more optimization.
11 174 0.395791313909 Henry Cohn, 2025, needs more optimization.
11 175 0.396712060503 Henry Cohn, 2025, needs more optimization.
11 176 0.398320474845 Henry Cohn, 2025, needs more optimization.
11 177 0.398807260566 Henry Cohn, 2026, needs more optimization.
11 178 0.400111193039 Henry Cohn, 2025, needs more optimization.
11 179 0.401138936288 Henry Cohn, 2026, needs more optimization.
11 180 0.401814944645 Henry Cohn, 2026, needs more optimization.
11 181 0.402834072497 Henry Cohn, 2025, needs more optimization.
11 182 0.404024048903 Henry Cohn, 2025, needs more optimization.
11 183 0.404473828764 Henry Cohn, 2025, needs more optimization.
11 184 0.405385624737 Henry Cohn, 2026, needs more optimization.
11 185 0.405516170418 Henry Cohn, 2026, needs more optimization.
11 186 0.406191917009 Henry Cohn, 2025, needs more optimization.
11 187 0.406636306148 Henry Cohn, 2025, needs more optimization.
11 188 0.406810650281 Henry Cohn, 2026, needs more optimization.
11 189 0.407525213298 Henry Cohn, 2026, needs more optimization.
11 190 0.408229117608 Henry Cohn, 2026, needs more optimization.
11 191 0.408891696594 Henry Cohn, 2026, needs more optimization.
11 192 0.409413416152 Henry Cohn, 2026, needs more optimization.
11 193 0.409973956997 Henry Cohn, 2026, needs more optimization.
11 194 0.410641931743 Henry Cohn, 2026, needs more optimization.
11 195 0.410908028917 Henry Cohn, 2026, needs more optimization.
11 196 0.411546245104 Henry Cohn, 2026, needs more optimization.
11 197 0.411563541077 Henry Cohn, 2026, needs more optimization.
11 198 0.412166825496 Henry Cohn, 2026, needs more optimization.
11 199 0.412661829407 Henry Cohn, 2026, needs more optimization.
11 200 0.412794093538 Henry Cohn, 2026, needs more optimization.
11 201 0.412895876164 Henry Cohn, 2026, needs more optimization.
11 202 0.413384010635 Henry Cohn, 2026, needs more optimization.
11 203 0.413847103567 Henry Cohn, 2026, needs more optimization.
11 204 0.414489862508 Henry Cohn, 2026, needs more optimization.
11 205 0.414758247814 Henry Cohn, 2026, needs more optimization.
11 206 0.415473084224 Henry Cohn, 2026, needs more optimization.
11 207 0.415610964613 Henry Cohn, 2026, needs more optimization.
11 208 0.416022762341 Henry Cohn, 2026, needs more optimization.
11 209 0.417189089166 Henry Cohn, 2026, needs more optimization.
11 210 0.417291027866 Henry Cohn, 2026, needs more optimization.
11 211 0.417959280166 Henry Cohn, 2026, needs more optimization.
11 212 0.418441903517 Henry Cohn, 2026, needs more optimization.
11 213 0.418776857352 Henry Cohn, 2026, needs more optimization.
11 214 0.419237880239 Henry Cohn, 2026, needs more optimization.
11 215 0.419984112437 Henry Cohn, 2026, needs more optimization.
11 216 0.420220472954 Henry Cohn, 2026, needs more optimization.
11 217 0.420854946831 Henry Cohn, 2026, needs more optimization.
11 218 0.421115627196 Henry Cohn, 2026, needs more optimization.
11 219 0.421860019173 Henry Cohn, 2026, needs more optimization.
11 220 0.422387510444 Henry Cohn, 2026, needs more optimization.
11 221 0.422953187802 Henry Cohn, 2026, needs more optimization.
11 222 0.423387422808 Henry Cohn, 2026, needs more optimization.
11 223 0.423737855406 Henry Cohn, 2026, needs more optimization.
11 224 0.423855689534 Henry Cohn, 2026, needs more optimization.
11 225 0.424282626872 Henry Cohn, 2026, needs more optimization.
11 227 0.424798964888 Henry Cohn, 2026, needs more optimization.
11 228 0.425263132645 Henry Cohn, 2026, needs more optimization.
11 229 0.425730816505 Henry Cohn, 2026, needs more optimization.
11 230 0.426310086126 Henry Cohn, 2026, needs more optimization.
11 231 0.426829251740 Henry Cohn, 2026, needs more optimization.
11 232 0.427184290541 Henry Cohn, 2026, needs more optimization.
11 233 0.427343615460 Henry Cohn, 2026, needs more optimization.
11 234 0.427754465305 Henry Cohn, 2026, needs more optimization.
11 235 0.428178914369 Henry Cohn, 2026, needs more optimization.
11 236 0.428610081603 Henry Cohn, 2026, needs more optimization.
11 237 0.428640653788 Henry Cohn, 2026, needs more optimization.
11 238 0.428806027244 Henry Cohn, 2026, needs more optimization.
11 239 0.429040628376 Henry Cohn, 2026, needs more optimization.
11 240 0.429098742027 Henry Cohn, 2025, needs more optimization.
11 241 0.429973355888 Henry Cohn, 2025, needs more optimization.
11 242 0.430928428639 Henry Cohn, 2026, needs more optimization.
11 243 0.432354797268 Henry Cohn, 2026, needs more optimization.
11 244 0.432603558084 Henry Cohn, 2026, needs more optimization.
11 245 0.432620932549 Henry Cohn, 2026, needs more optimization.
11 246 0.433233245052 Henry Cohn, 2026, needs more optimization.
11 247 0.433610805513 Henry Cohn, 2026, needs more optimization.
11 248 0.434145308382 Henry Cohn, 2026, needs more optimization.
11 249 0.435006394286 Henry Cohn, 2026, needs more optimization.
11 250 0.437697146612 Henry Cohn, 2026, needs more optimization.
11 251 0.437744973709 Henry Cohn, 2026, needs more optimization.
11 252 0.437751154860 Henry Cohn, 2026, needs more optimization.
11 253 0.437987871131 Henry Cohn, 2026, needs more optimization.
11 254 0.438011072834 Henry Cohn, 2026, needs more optimization.
11 255 0.438876428807 Henry Cohn, 2026, needs more optimization.
11 256 0.438958419338 Henry Cohn, 2026, needs more optimization.
11 257 0.439482788001 Henry Cohn, 2026, needs more optimization.
11 258 0.439582725446 Henry Cohn, 2026, needs more optimization.
11 259 0.440625030991 Henry Cohn, 2026, needs more optimization.
11 260 0.440640903720 Henry Cohn, 2026, needs more optimization.
11 261 0.440833425178 Henry Cohn, 2026, needs more optimization.
11 262 0.440866174416 Henry Cohn, 2026, needs more optimization.
11 263 0.440946596287 Henry Cohn, 2026, needs more optimization.
11 264 0.440968477193 Henry Cohn, 2026, needs more optimization.
11 265 0.440994816052 Henry Cohn, 2026, needs more optimization.
11 266 0.441320475867 Henry Cohn, 2026, needs more optimization.
11 267 0.441370306663 Henry Cohn, 2026, needs more optimization.
11 268 0.441429635857 Henry Cohn, 2026, needs more optimization.
11 269 0.442518769590 Henry Cohn, 2026, needs more optimization.
11 270 0.442557055621 Henry Cohn, 2026, needs more optimization.
11 271 0.442743424981 Henry Cohn, 2026, needs more optimization.
11 272 0.443016067299 Henry Cohn, 2026, needs more optimization.
11 273 0.443092684846 Henry Cohn, 2026, needs more optimization.
11 274 0.443114814092 Henry Cohn, 2026, needs more optimization.
11 275 0.443268846145 Henry Cohn, 2026, needs more optimization.
11 276 0.443748138008 Henry Cohn, 2026, needs more optimization.
11 277 0.443777633208 Henry Cohn, 2026, needs more optimization.
11 278 0.444838011725 Henry Cohn, 2026, needs more optimization.
11 279 0.444852397481 Henry Cohn, 2026, needs more optimization.
11 280 0.445590332885 Henry Cohn, 2026, needs more optimization.
11 281 0.445679295848 Henry Cohn, 2026, needs more optimization.
11 282 0.446793868294 Henry Cohn, 2026, needs more optimization.
11 283 0.447200862398 Henry Cohn, 2026, needs more optimization.
11 284 0.447212698987 Henry Cohn, 2026, needs more optimization.
11 285 0.447227399440 Henry Cohn, 2026, needs more optimization.
11 286 0.447240900911 Henry Cohn, 2026, needs more optimization.
11 289 0.447266123833 Henry Cohn, 2026, needs more optimization.
11 290 0.448535371375 Henry Cohn, 2026, needs more optimization.
11 291 0.449410970035 Henry Cohn, 2026, needs more optimization.
11 292 0.449459638926 Henry Cohn, 2026, needs more optimization.
11 293 0.449602715871 Henry Cohn, 2026, needs more optimization.
11 294 0.449609561912 Henry Cohn, 2026, needs more optimization.
11 295 0.450711720752 Henry Cohn, 2026, needs more optimization.
11 296 0.451526964848 Henry Cohn, 2026, needs more optimization.
11 297 0.454535253827 Henry Cohn, 2026, needs more optimization.
11 298 0.458129466397 Henry Cohn, 2026, needs more optimization.
11 299 0.458858549866 Henry Cohn, 2026, needs more optimization.
11 300 0.459021622171 Henry Cohn, 2026, needs more optimization.
11 301 0.459639328973 Henry Cohn, 2025, needs more optimization.
11 302 0.460203223454 Henry Cohn, 2025, needs more optimization.
11 303 0.460288477586 Henry Cohn, 2025, needs more optimization.
11 304 0.460862225321 Henry Cohn, 2026, needs more optimization.
11 305 0.461268830255 Henry Cohn, 2025, needs more optimization.
11 306 0.461721343172 Henry Cohn, 2025, needs more optimization.
11 307 0.462044048096 Henry Cohn, 2025, needs more optimization.
11 308 0.462383050078 Henry Cohn, 2026, needs more optimization.
11 309 0.462994444527 Henry Cohn, 2025, needs more optimization.
11 310 0.463544165000 Henry Cohn, 2025, needs more optimization.
11 311 0.463659643751 Henry Cohn, 2025, needs more optimization.
11 312 0.464359894912 Henry Cohn, 2026, needs more optimization.
11 313 0.464976892208 Henry Cohn, 2025, needs more optimization.
11 314 0.465091025246 Henry Cohn, 2025, needs more optimization.
11 315 0.465715320515 Henry Cohn, 2025, needs more optimization.
11 316 0.465897384515 Henry Cohn, 2026, needs more optimization.
11 317 0.465904310823 Henry Cohn, 2025, needs more optimization.
11 318 0.466097303368 Henry Cohn, 2025, needs more optimization.
11 319 0.466267282465 Henry Cohn, 2025, needs more optimization.
11 320 0.467028400033 Henry Cohn, 2026, needs more optimization.
11 321 0.467258854327 Henry Cohn, 2025, needs more optimization.
11 322 0.467511739233 Henry Cohn, 2025, needs more optimization.
11 323 0.468182878263 Henry Cohn, 2025, needs more optimization.
11 324 0.470460066007 Henry Cohn, 2026, needs more optimization.
11 325 0.471201521874 Henry Cohn, 2025, needs more optimization.
11 326 0.471702531797 Henry Cohn, 2025, needs more optimization.
11 327 0.471894887006 Henry Cohn, 2025, needs more optimization.
11 328 0.472633915840 Henry Cohn, 2026, needs more optimization.
11 329 0.472833096322 Henry Cohn, 2025, needs more optimization.
11 330 0.473098656858 Henry Cohn, 2025, needs more optimization.
11 331 0.473467506404 Henry Cohn, 2025, needs more optimization.
11 332 0.473850864192 Henry Cohn, 2026, needs more optimization.
11 333 0.473871803646 Henry Cohn, 2025, needs more optimization.
11 334 0.474236401896 Henry Cohn, 2025, needs more optimization.
11 335 0.474719431936 Henry Cohn, 2025, needs more optimization.
11 336 0.474724651842 Henry Cohn, 2026, needs more optimization.
11 337 0.475243110879 Henry Cohn, 2025, needs more optimization.
11 338 0.475609826115 Henry Cohn, 2025, needs more optimization.
11 339 0.475701250198 Henry Cohn, 2025, needs more optimization.
11 340 0.475915208916 Henry Cohn, 2026, needs more optimization.
11 341 0.476285444701 Henry Cohn, 2025, needs more optimization.
11 342 0.476354680116 Henry Cohn, 2025, needs more optimization.
11 343 0.476618421655 Henry Cohn, 2025, needs more optimization.
11 344 0.476716590023 Henry Cohn, 2026, needs more optimization.
11 345 0.476956469542 Henry Cohn, 2025, needs more optimization.
11 346 0.477307252247 Henry Cohn, 2025, needs more optimization.
11 347 0.478281760346 Henry Cohn, 2025, needs more optimization.
11 348 0.478297176307 Henry Cohn, 2026, needs more optimization.
11 349 0.479176122649 Henry Cohn, 2025, needs more optimization.
11 350 0.479210833472 Henry Cohn, 2025, needs more optimization.
11 351 0.479489173418 Henry Cohn, 2025, needs more optimization.
11 352 0.479982048056 Henry Cohn, 2025, needs more optimization.
11 353 0.480077140051 Henry Cohn, 2025, needs more optimization.
11 354 0.480183713218 Henry Cohn, 2025, needs more optimization.
11 355 0.480436888208 Henry Cohn, 2025, needs more optimization.
11 356 0.480487166888 Henry Cohn, 2025, needs more optimization.
11 357 0.480842494444 Henry Cohn, 2025, needs more optimization.
11 358 0.480902210072 Henry Cohn, 2025, needs more optimization.
11 359 0.481274495959 Henry Cohn, 2025, needs more optimization.
11 360 0.481291506240 Henry Cohn, 2025, needs more optimization.
11 361 0.481741529691 Henry Cohn, 2025, needs more optimization.
11 362 0.481995028899 Henry Cohn, 2025, needs more optimization.
11 363 0.482103941912 Henry Cohn, 2025, needs more optimization.
11 364 0.482276232393 Henry Cohn, 2026, needs more optimization.
11 365 0.482303853060 Henry Cohn, 2025, needs more optimization.
11 366 0.482501512317 Henry Cohn, 2025, needs more optimization.
11 367 0.483057849632 Henry Cohn, 2025, needs more optimization.
11 368 0.483246288551 Henry Cohn, 2026, needs more optimization.
11 369 0.483262726267 Henry Cohn, 2025, needs more optimization.
11 370 0.483583948555 Henry Cohn, 2025, needs more optimization.
11 371 0.483706899316 Henry Cohn, 2025, needs more optimization.
11 372 0.483716473185 Henry Cohn, 2026, needs more optimization.
11 373 0.484043235518 Henry Cohn, 2025, needs more optimization.
11 374 0.484097153813 Henry Cohn, 2025, needs more optimization.
11 376 0.484538913691 Henry Cohn, 2026, needs more optimization.
11 377 0.485141337715 Henry Cohn, 2025, needs more optimization.
11 378 0.485150414751 Henry Cohn, 2025, needs more optimization.
11 379 0.485977589895 Henry Cohn, 2025, needs more optimization.
11 380 0.485977720696 Henry Cohn, 2026, needs more optimization.
11 381 0.486020085020 Henry Cohn, 2025, needs more optimization.
11 382 0.486040770663 Henry Cohn, 2025, needs more optimization.
11 383 0.486097954624 Henry Cohn, 2025, needs more optimization.
11 384 0.486113457975 Henry Cohn, 2026, needs more optimization.
11 385 0.486126091016 Henry Cohn, 2025, needs more optimization.
11 386 0.486381949776 Henry Cohn, 2025, needs more optimization.
11 387 0.486469389022 Henry Cohn, 2025, needs more optimization.
11 388 0.486486010528 Henry Cohn, 2025, needs more optimization.
11 389 0.486579853534 Henry Cohn, 2025, needs more optimization.
11 390 0.486591059814 Henry Cohn, 2025, needs more optimization.
11 392 0.487378958415 Henry Cohn, 2026, needs more optimization.
11 393 0.487401897134 Henry Cohn, 2025, needs more optimization.
11 394 0.487409887893 Henry Cohn, 2025, needs more optimization.
11 395 0.487417126467 Henry Cohn, 2025, needs more optimization.
11 396 0.487482175882 Henry Cohn, 2026, needs more optimization.
11 397 0.488352351257 Henry Cohn, 2026, needs more optimization.
11 398 0.488437617194 Henry Cohn, 2025, needs more optimization.
11 400 0.488675285089 Henry Cohn, 2026, needs more optimization.
11 401 0.490210887347 Henry Cohn, 2026, needs more optimization.
11 403 0.490210887455 Henry Cohn, 2025, needs more optimization.
11 404 0.490239534679 Henry Cohn, 2025, needs more optimization.
11 405 0.490253634370 Henry Cohn, 2025, needs more optimization.
11 406 0.491282760871 Henry Cohn, 2025, needs more optimization.
11 408 0.491614827339 Henry Cohn, 2026, needs more optimization.
11 409 0.491734488110 Henry Cohn, 2025, needs more optimization.
11 410 0.492513510937 Henry Cohn, 2026, needs more optimization.
11 411 0.492513511025 Henry Cohn, 2025, needs more optimization.
11 412 0.492596937457 Henry Cohn, 2026, needs more optimization.
11 415 0.492734383686 Henry Cohn, 2026, needs more optimization.
11 416 0.492812844913 Henry Cohn, 2026, needs more optimization.
11 417 0.492828395878 Henry Cohn, 2025, needs more optimization.
11 418 0.493129409762 Henry Cohn, 2026, needs more optimization.
11 419 0.493274992243 Henry Cohn, 2026, needs more optimization.
11 421 0.493916610675 Henry Cohn, 2026, needs more optimization.
11 422 0.493945089141 Henry Cohn, 2025, needs more optimization.
11 423 0.493970791475 Henry Cohn, 2025, needs more optimization.
11 424 0.493985756792 Henry Cohn, 2025, needs more optimization.
11 425 0.494037829338 Henry Cohn, 2025, needs more optimization.
11 426 0.494051876349 Henry Cohn, 2025, needs more optimization.
11 427 0.494082410490 Henry Cohn, 2026, needs more optimization.
11 429 0.494119524472 Henry Cohn, 2026, needs more optimization.
11 430 0.494207621254 Henry Cohn, 2026, needs more optimization.
11 431 0.494208897310 Henry Cohn, 2026, needs more optimization.
11 432 0.494214749693 Henry Cohn, 2026, needs more optimization.
11 434 0.494311598236 Henry Cohn, 2025, needs more optimization.
11 435 0.494313766122 Henry Cohn, 2025, needs more optimization.
11 436 0.494531349276 Henry Cohn, 2026, needs more optimization.
11 438 0.494865572262 Henry Cohn, 2025, needs more optimization.
11 439 0.494939689263 Henry Cohn, 2026, needs more optimization.
11 440 0.495001803697 Henry Cohn, 2025, needs more optimization.
11 441 0.495208013246 Henry Cohn, 2025, needs more optimization.
11 442 0.495240503799 Henry Cohn, 2026, needs more optimization.
11 443 0.495240503803 Henry Cohn, 2026, needs more optimization.
11 445 0.496354649532 Henry Cohn, 2026, needs more optimization.
11 446 0.496423782539 Henry Cohn, 2025, needs more optimization.
11 449 0.496522031081 Henry Cohn, 2026, needs more optimization.
11 450 0.496883465367 Henry Cohn, 2025, needs more optimization.
11 451 0.496942224687 Henry Cohn, 2026, needs more optimization.
11 452 0.496973862488 Henry Cohn, 2026, needs more optimization.
11 472 0.499957673075 Henry Cohn, 2025, needs more optimization.
11 593 0.499999989608 A. Novikov, N. Vu, M. Eisenberger, E. Dupont, P.-S. Huang, A. Z. Wagner, S. Shirobokov, B. Kozlovskii, F. J. R. Ruiz, A. Mehrabian, M. P. Kumar, A. See, S. Chaudhuri, G. Holland, A. Davies, S. Nowozin, P. Kohli, and M. Balog, AlphaEvolve: A coding agent for scientific and algorithmic discovery, Google DeepMind white paper, 2025, after some further optimization.
11 594 0.500141289029 Ilmari Vahteristo, 2026.
11 595 0.500925697544 Ilmari Vahteristo, 2026.
11 596 0.501441454208 Henry Cohn, 2026, needs more optimization.
11 597 0.520255490104 Henry Cohn, 2025, needs more optimization.
11 598 0.520331537319 Henry Cohn, 2025, needs more optimization.
11 600 0.520405377653 Henry Cohn, 2026, needs more optimization.
11 604 0.521043245819 Henry Cohn, 2026, needs more optimization.
11 605 0.521318118650 Henry Cohn, 2026, needs more optimization.
11 606 0.521353070721 Henry Cohn, 2026, needs more optimization.
11 608 0.521425128897 Henry Cohn, 2026, needs more optimization.
11 609 0.521600438331 Henry Cohn, 2026, needs more optimization.
11 611 0.521854890548 Henry Cohn, 2025, needs more optimization.
11 612 0.523617017905 Henry Cohn, 2026, needs more optimization.
11 616 0.523839473739 Henry Cohn, 2026, needs more optimization.
11 617 0.524032119163 Henry Cohn, 2025, needs more optimization.
11 620 0.524033456003 Henry Cohn, 2026, needs more optimization.
11 621 0.524091054566 Henry Cohn, 2025, needs more optimization.
11 623 0.524096196647 Henry Cohn, 2025, needs more optimization.
11 624 0.525155603305 Henry Cohn, 2026, needs more optimization.
11 628 0.525283801910 Henry Cohn, 2026, needs more optimization.
11 630 0.525675334247 Henry Cohn, 2026, needs more optimization.
11 631 0.525682491562 Henry Cohn, 2025, needs more optimization.
11 632 0.525941594293 Henry Cohn, 2026, needs more optimization.
11 633 0.527485789217 Henry Cohn, 2025, needs more optimization.
11 636 0.527549701492 Henry Cohn, 2026, needs more optimization.
11 637 0.527569511004 Henry Cohn, 2025, needs more optimization.
11 640 0.528850538035 Henry Cohn, 2026, needs more optimization.
11 644 0.529185588858 Henry Cohn, 2026, needs more optimization.
11 646 0.529335846381 Henry Cohn, 2025, needs more optimization.
11 647 0.530846594391 Henry Cohn, 2025, needs more optimization.
11 648 0.530881393746 Henry Cohn, 2026, needs more optimization.
11 649 0.531044621234 Henry Cohn, 2025, needs more optimization.
11 650 0.531139104296 Henry Cohn, 2025, needs more optimization.
11 652 0.532332389863 Henry Cohn, 2026, needs more optimization.
11 653 0.532366999013 Henry Cohn, 2025, needs more optimization.
11 656 0.532386749828 Henry Cohn, 2026, needs more optimization.
11 657 0.532392160573 Henry Cohn, 2025, needs more optimization.
11 658 0.532401095302 Henry Cohn, 2025, needs more optimization.
11 659 0.532467715439 Henry Cohn, 2025, needs more optimization.
11 660 0.532683682665 Henry Cohn, 2026, needs more optimization.
11 661 0.534392831481 Henry Cohn, 2025, needs more optimization.
11 662 0.534401715093 Henry Cohn, 2025, needs more optimization.
11 663 0.534422746084 Henry Cohn, 2025, needs more optimization.
11 664 0.535698338176 Henry Cohn, 2026, needs more optimization.
11 665 0.535702593944 Henry Cohn, 2025, needs more optimization.
11 666 0.535725882319 Henry Cohn, 2025, needs more optimization.
11 667 0.535746493888 Henry Cohn, 2025, needs more optimization.
11 668 0.536717879016 Henry Cohn, 2026, needs more optimization.
11 669 0.536758892961 Henry Cohn, 2025, needs more optimization.
11 670 0.536786559175 Henry Cohn, 2025, needs more optimization.
11 672 0.536789415949 Henry Cohn, 2026, needs more optimization.
11 673 0.536806501096 Henry Cohn, 2025, needs more optimization.
11 676 0.539142438831 Henry Cohn, 2026, needs more optimization.
11 677 0.539251824581 Henry Cohn, 2025, needs more optimization.
11 678 0.539285306592 Henry Cohn, 2026, needs more optimization.
11 679 0.539314255561 Henry Cohn, 2026, needs more optimization.
11 680 0.539330726828 Henry Cohn, 2026, needs more optimization.
11 681 0.539565443765 Henry Cohn, 2026, needs more optimization.
11 682 0.541582375258 Henry Cohn, 2026, needs more optimization.
11 683 0.541618940674 Henry Cohn, 2025, needs more optimization.
11 684 0.541626134008 Henry Cohn, 2026, needs more optimization.
11 686 0.541652564397 Henry Cohn, 2026, needs more optimization.
11 687 0.541917098259 Henry Cohn, 2025, needs more optimization.
11 688 0.542939046711 Henry Cohn, 2026, needs more optimization.
11 690 0.543023508841 Henry Cohn, 2026, needs more optimization.
11 692 0.543069833915 Henry Cohn, 2026, needs more optimization.
11 693 0.543396266703 Henry Cohn, 2026, needs more optimization.
11 694 0.545955087139 Henry Cohn, 2026, needs more optimization.
11 695 0.545969774608 Henry Cohn, 2025, needs more optimization.
11 696 0.546017681485 Henry Cohn, 2026, needs more optimization.
11 697 0.546071440016 Henry Cohn, 2025, needs more optimization.
11 698 0.546903607132 Henry Cohn, 2026, needs more optimization.
11 699 0.546915672479 Henry Cohn, 2025, needs more optimization.
11 700 0.546970395971 Henry Cohn, 2026, needs more optimization.
11 701 0.547105417013 Henry Cohn, 2025, needs more optimization.
11 702 0.549143958357 Henry Cohn, 2026, needs more optimization.
11 703 0.550249089558 Henry Cohn, 2025, needs more optimization.
11 982 0.555555555556 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−5
11 983 0.588808434262 Henry Cohn, 2025, needs more optimization.
11 984 0.588842803390 Henry Cohn, 2026, needs more optimization.
11 985 0.589065956887 Henry Cohn, 2025, needs more optimization.
11 986 0.589074288260 Henry Cohn, 2026, needs more optimization.
11 987 0.589337788121 Henry Cohn, 2025, needs more optimization.
11 988 0.589474269186 Henry Cohn, 2026, needs more optimization.
11 990 0.589483899310 Henry Cohn, 2026, needs more optimization.
11 991 0.589724651603 Henry Cohn, 2025, needs more optimization.
11 992 0.589729337081 Henry Cohn, 2026, needs more optimization.
11 993 0.589747194595 Henry Cohn, 2025, needs more optimization.
11 994 0.589775579041 Henry Cohn, 2026, needs more optimization.
11 996 0.589929252049 Henry Cohn, 2026, needs more optimization.
11 997 0.590217455898 Henry Cohn, 2025, needs more optimization.
11 998 0.590283232759 Henry Cohn, 2026, needs more optimization.
11 999 0.590290163347 Henry Cohn, 2025, needs more optimization.
11 1000 0.590342544738 Henry Cohn, 2026, needs more optimization.
11 1001 0.590366225530 Henry Cohn, 2025, needs more optimization.
11 1002 0.590628709920 Henry Cohn, 2025, needs more optimization.
11 1003 0.590659823164 Henry Cohn, 2025, needs more optimization.
11 1004 0.590674113006 Henry Cohn, 2026, needs more optimization.
11 1005 0.590861588302 Henry Cohn, 2026, needs more optimization.
11 1006 0.590979127066 Henry Cohn, 2026, needs more optimization.
11 1007 0.591030480092 Henry Cohn, 2025, needs more optimization.
11 1008 0.591238716992 Henry Cohn, 2026, needs more optimization.
11 1009 0.591282497506 Henry Cohn, 2025, needs more optimization.
11 1010 0.591399096240 Henry Cohn, 2026, needs more optimization.
11 1011 0.591405377429 Henry Cohn, 2025, needs more optimization.
11 1012 0.591437856314 Henry Cohn, 2026, needs more optimization.
11 1013 0.591631264119 Henry Cohn, 2025, needs more optimization.
11 1014 0.591652512963 Henry Cohn, 2026, needs more optimization.
11 1015 0.591883276887 Henry Cohn, 2025, needs more optimization.
11 1016 0.591904113557 Henry Cohn, 2026, needs more optimization.
11 1017 0.591917458356 Henry Cohn, 2025, needs more optimization.
11 1018 0.592152389992 Henry Cohn, 2026, needs more optimization.
11 1019 0.592164252037 Henry Cohn, 2025, needs more optimization.
11 1020 0.592205871152 Henry Cohn, 2026, needs more optimization.
11 1021 0.592232252111 Henry Cohn, 2026, needs more optimization.
11 1022 0.592579532885 Henry Cohn, 2026, needs more optimization.
11 1023 0.592595642913 Henry Cohn, 2025, needs more optimization.
11 1024 0.592628472863 Henry Cohn, 2026, needs more optimization.
12 25 0.061281914575 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
1200⁢x3−144⁢x2−12⁢x+1
12 26 0.071428571429 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
14⁢x−1
12 27 0.074764926182 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
12 28 0.082592206268 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
12 29 0.084348009310 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
496⁢x4+92⁢x3−57⁢x2−8⁢x+1
12 30 0.089146601434 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
3856⁢x4+1456⁢x3+100⁢x2−12⁢x−1
12 31 0.098704091241 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
863⁢x2+6⁢x−9
12 32 0.098704091241 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
863⁢x2+6⁢x−9
12 34 0.112004618870 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
44⁢x2+4⁢x−1
12 35 0.119914058434 Henry Cohn, 2025.
12 36 0.121730661114 Henry Cohn, 2026.
12 37 0.121971459128 Henry Cohn, 2023.
359⁢x2+30⁢x−9
12 38 0.130785955647 Henry Cohn, 2026.
12 39 0.132497435001 Henry Cohn, 2023.
12 40 0.133638243588 Henry Cohn, 2023.
12 41 0.135922539556 Henry Cohn, 2023.
12 42 0.136597789057 Henry Cohn, 2023.
5296⁢x4+1248⁢x3−40⁢x2−24⁢x−1
12 43 0.139595542735 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
12 44 0.141964936980 Henry Cohn, 2023.
736256⁢x8−133120⁢x7−146176⁢x6−13824⁢x5+8368⁢x4+1568⁢x3−72⁢x2−24⁢x−1
12 45 0.149653254074 Henry Cohn, 2024.
12 46 0.150221879934 Henry Cohn, 2025.
12 50 0.150442862439 Henry Cohn, 2023.
956⁢x2−84⁢x−9
12 51 0.159810400056 Henry Cohn, 2023.
3600⁢x5−1080⁢x4−252⁢x3+36⁢x2+9⁢x−1
12 52 0.180095470186 Henry Cohn, 2025.
12 53 0.187411648808 Henry Cohn, 2025.
12 54 0.189746662791 Henry Cohn, 2024.
12 55 0.193319611131 Henry Cohn, 2025.
12 56 0.200925636261 Henry Cohn, 2025.
12 57 0.201958116645 Henry Cohn, 2025.
12 58 0.203749632752 Henry Cohn, 2025.
12 59 0.205147720753 Henry Cohn, 2025.
12 60 0.207643910372 Henry Cohn, 2026, needs more optimization.
12 61 0.211404126394 Henry Cohn, 2025.
12 62 0.213863503460 Henry Cohn, 2025.
12 63 0.213962909655 Henry Cohn, 2026, needs more optimization.
12 64 0.214090056231 Henry Cohn, 2026, needs more optimization.
12 65 0.214410531368 Henry Cohn, 2026, needs more optimization.
12 66 0.215064206569 Henry Cohn, 2026, needs more optimization.
12 67 0.220118787411 Henry Cohn, 2026, needs more optimization.
12 68 0.222608836393 Henry Cohn, 2026, needs more optimization.
12 69 0.225802384453 Henry Cohn, 2026, needs more optimization.
12 70 0.228644883302 Henry Cohn, 2026, needs more optimization.
12 71 0.232255775950 Henry Cohn, 2025.
12 72 0.233344424897 Henry Cohn, 2026.
12 73 0.234628999325 Henry Cohn, 2026, needs more optimization.
12 74 0.235166207807 Henry Cohn, 2026, needs more optimization.
12 75 0.236566313789 Henry Cohn, 2026, needs more optimization.
12 76 0.237336218342 Henry Cohn, 2025.
12 77 0.237968057446 Henry Cohn, 2025.
12 78 0.241648057068 Henry Cohn, 2025.
12 79 0.243234050771 Henry Cohn, 2025.
12 80 0.247423227496 Henry Cohn, 2026, needs more optimization.
12 81 0.25 C. Ma, T. T. Zhaowei, P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
4⁢x−1
12 82 0.255753795402 Henry Cohn, 2026, needs more optimization.
12 83 0.258657193037 Henry Cohn, 2026, needs more optimization.
12 84 0.259079120305 Henry Cohn, 2026, needs more optimization.
12 85 0.260700618907 Henry Cohn, 2026, needs more optimization.
12 86 0.261584332921 Henry Cohn, 2026, needs more optimization.
12 87 0.261666113899 Henry Cohn, 2026, needs more optimization.
12 88 0.261873213364 Henry Cohn, 2026, needs more optimization.
12 89 0.262213741970 Henry Cohn, 2026, needs more optimization.
12 90 0.262685089966 Henry Cohn, 2026, needs more optimization.
12 91 0.263153154395 Henry Cohn, 2026, needs more optimization.
12 92 0.263539603169 Henry Cohn, 2026, needs more optimization.
12 93 0.264145863655 Henry Cohn, 2026, needs more optimization.
12 94 0.265194206852 Henry Cohn, 2026, needs more optimization.
12 95 0.265548936855 Henry Cohn, 2026, needs more optimization.
12 96 0.265982067744 Henry Cohn, 2026, needs more optimization.
12 97 0.266109762761 Henry Cohn, 2026, needs more optimization.
12 98 0.266808143783 Henry Cohn, 2026, needs more optimization.
12 100 0.267113377119 Henry Cohn, 2026, needs more optimization.
12 101 0.267198319814 Henry Cohn, 2026, needs more optimization.
12 102 0.267201610320 Henry Cohn, 2026, needs more optimization.
12 103 0.269832699377 Henry Cohn, 2026, needs more optimization.
12 104 0.271860966378 Henry Cohn, 2026, needs more optimization.
12 105 0.273461339500 Henry Cohn, 2026, needs more optimization.
12 106 0.274917636997 Henry Cohn, 2026, needs more optimization.
12 107 0.276917906014 Henry Cohn, 2026, needs more optimization.
12 108 0.276965352595 Henry Cohn, 2026, needs more optimization.
12 109 0.277603311786 Henry Cohn, 2026, needs more optimization.
12 110 0.278352312623 Henry Cohn, 2026, needs more optimization.
12 111 0.278780094721 Henry Cohn, 2026, needs more optimization.
12 112 0.281101493533 Henry Cohn, 2026, needs more optimization.
12 113 0.282021066887 Henry Cohn, 2026, needs more optimization.
12 114 0.291611802601 Henry Cohn, 2026, needs more optimization.
12 115 0.292493200735 Henry Cohn, 2026, needs more optimization.
12 116 0.293189008248 Henry Cohn, 2026, needs more optimization.
12 117 0.294031290192 Henry Cohn, 2026, needs more optimization.
12 118 0.294318328878 Henry Cohn, 2026, needs more optimization.
12 120 0.294708984746 Henry Cohn, 2026, needs more optimization.
12 121 0.294708984748 Henry Cohn, 2026, needs more optimization.
12 122 0.304154401283 Henry Cohn, 2026, needs more optimization.
12 123 0.305712625663 Henry Cohn, 2026, needs more optimization.
12 124 0.305740747326 Henry Cohn, 2026, needs more optimization.
12 125 0.305884478708 Henry Cohn, 2026, needs more optimization.
12 126 0.306653138440 Henry Cohn, 2026, needs more optimization.
12 127 0.307716181568 Henry Cohn, 2026, needs more optimization.
12 128 0.308118108015 Henry Cohn, 2026, needs more optimization.
12 129 0.309039276967 Henry Cohn, 2026, needs more optimization.
12 130 0.310042584977 Henry Cohn, 2026, needs more optimization.
12 131 0.310611618140 Henry Cohn, 2026, needs more optimization.
12 132 0.314077437468 Henry Cohn, 2026, needs more optimization.
12 133 0.317037278561 Henry Cohn, 2026, needs more optimization.
12 134 0.317394821581 Henry Cohn, 2026, needs more optimization.
12 135 0.318249108802 Henry Cohn, 2026, needs more optimization.
12 136 0.318840926164 Henry Cohn, 2026, needs more optimization.
12 137 0.320444473048 Henry Cohn, 2026, needs more optimization.
12 138 0.322210297758 Henry Cohn, 2026, needs more optimization.
12 139 0.322266997399 Henry Cohn, 2026, needs more optimization.
12 140 0.322387362910 Henry Cohn, 2026, needs more optimization.
12 141 0.322672872105 Henry Cohn, 2026, needs more optimization.
12 142 0.322936703966 Henry Cohn, 2026, needs more optimization.
12 143 0.323138043691 Henry Cohn, 2026, needs more optimization.
12 144 0.323768007807 Henry Cohn, 2026, needs more optimization.
12 145 0.324207225171 Henry Cohn, 2026, needs more optimization.
12 146 0.324331025508 Henry Cohn, 2026, needs more optimization.
12 147 0.324845922285 Henry Cohn, 2026, needs more optimization.
12 148 0.325225308691 Henry Cohn, 2026, needs more optimization.
12 149 0.325540813445 Henry Cohn, 2026, needs more optimization.
12 150 0.326790061973 Henry Cohn, 2026, needs more optimization.
12 151 0.327152196741 Henry Cohn, 2026, needs more optimization.
12 152 0.327641655930 Henry Cohn, 2026, needs more optimization.
12 153 0.328491673622 Henry Cohn, 2026, needs more optimization.
12 154 0.329005175892 Henry Cohn, 2026, needs more optimization.
12 155 0.329460178070 Henry Cohn, 2026, needs more optimization.
12 156 0.329662053655 Henry Cohn, 2026, needs more optimization.
12 157 0.329880841682 Henry Cohn, 2026, needs more optimization.
12 158 0.330020811470 Henry Cohn, 2026, needs more optimization.
12 159 0.330026319111 Henry Cohn, 2026, needs more optimization.
12 160 0.330027572668 Henry Cohn, 2026, needs more optimization.
12 161 0.330064480261 Henry Cohn, 2026, needs more optimization.
12 162 0.331403287521 Henry Cohn, 2026, needs more optimization.
12 163 0.331524578950 Henry Cohn, 2026, needs more optimization.
12 164 0.331691650682 Henry Cohn, 2026, needs more optimization.
12 165 0.332062489938 Henry Cohn, 2026, needs more optimization.
12 166 0.332679518472 Henry Cohn, 2026, needs more optimization.
12 167 0.332835294745 Henry Cohn, 2026, needs more optimization.
12 168 0.332860991124 Henry Cohn, 2026, needs more optimization.
12 169 0.332943961443 Henry Cohn, 2026, needs more optimization.
12 170 0.333013371069 Henry Cohn, 2026, needs more optimization.
12 171 0.333047165126 Henry Cohn, 2026, needs more optimization.
12 172 0.333093669072 Henry Cohn, 2026, needs more optimization.
12 173 0.333168057698 Henry Cohn, 2026, needs more optimization.
12 174 0.333168429568 Henry Cohn, 2026, needs more optimization.
12 176 0.333197038842 Henry Cohn, 2026, needs more optimization.
12 177 0.333221697815 Henry Cohn, 2026, needs more optimization.
12 178 0.333256860380 Henry Cohn, 2026, needs more optimization.
12 179 0.333907699235 Henry Cohn, 2026, needs more optimization.
12 180 0.336269891292 Henry Cohn, 2026, needs more optimization.
12 181 0.349037134271 Henry Cohn, 2026, needs more optimization.
12 182 0.351254810089 Henry Cohn, 2026, needs more optimization.
12 183 0.352993573868 Henry Cohn, 2026, needs more optimization.
12 184 0.353916612681 Henry Cohn, 2026, needs more optimization.
12 185 0.355686119816 Henry Cohn, 2026, needs more optimization.
12 186 0.356218768145 Henry Cohn, 2026, needs more optimization.
12 187 0.356819878701 Henry Cohn, 2026, needs more optimization.
12 188 0.358896803687 Henry Cohn, 2026, needs more optimization.
12 189 0.359542173661 Henry Cohn, 2026, needs more optimization.
12 190 0.360055774898 Henry Cohn, 2026, needs more optimization.
12 191 0.360945443125 Henry Cohn, 2026, needs more optimization.
12 192 0.361734431281 Henry Cohn, 2026, needs more optimization.
12 193 0.362179282020 Henry Cohn, 2026, needs more optimization.
12 194 0.362327157361 Henry Cohn, 2026, needs more optimization.
12 195 0.364330490630 Henry Cohn, 2026, needs more optimization.
12 196 0.366719121945 Henry Cohn, 2026, needs more optimization.
12 197 0.367033533392 Henry Cohn, 2026, needs more optimization.
12 198 0.367762987582 Henry Cohn, 2026, needs more optimization.
12 199 0.369404557276 Henry Cohn, 2026, needs more optimization.
12 200 0.369912654267 Henry Cohn, 2026, needs more optimization.
12 201 0.371170228907 Henry Cohn, 2026, needs more optimization.
12 202 0.372270385081 Henry Cohn, 2026, needs more optimization.
12 210 0.375 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001, Appendix D.12.12. The appendix lists the code size as 209, but the construction works just as well for 210.
8⁢x−3
12 211 0.378110897165 Henry Cohn, 2026, needs more optimization.
12 212 0.381927651344 Henry Cohn, 2026, needs more optimization.
12 213 0.382766114934 Henry Cohn, 2026, needs more optimization.
12 214 0.382957655758 Henry Cohn, 2026, needs more optimization.
12 215 0.383355513448 Henry Cohn, 2026, needs more optimization.
12 216 0.384413738493 Henry Cohn, 2026, needs more optimization.
12 217 0.385158396355 Henry Cohn, 2026, needs more optimization.
12 218 0.385726307848 Henry Cohn, 2026, needs more optimization.
12 219 0.386699369017 Henry Cohn, 2026, needs more optimization.
12 220 0.387261977326 Henry Cohn, 2026, needs more optimization.
12 223 0.392659642924 Henry Cohn, 2026, needs more optimization.
12 224 0.394012062949 Henry Cohn, 2026, needs more optimization.
12 225 0.394101016972 Henry Cohn, 2026, needs more optimization.
12 226 0.394108358740 Henry Cohn, 2026, needs more optimization.
12 227 0.394924076574 Henry Cohn, 2025, needs more optimization.
12 228 0.394926385731 Henry Cohn, 2026, needs more optimization.
12 229 0.395023232683 Henry Cohn, 2026, needs more optimization.
12 230 0.395104309471 Henry Cohn, 2025, needs more optimization.
12 231 0.395165390251 Henry Cohn, 2026, needs more optimization.
12 232 0.395426138850 Henry Cohn, 2025, needs more optimization.
12 233 0.395438351667 Henry Cohn, 2025, needs more optimization.
12 288 0.4 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
12 289 0.429257726236 Henry Cohn, 2026, needs more optimization.
12 290 0.429516989942 Henry Cohn, 2026, needs more optimization.
12 291 0.429724400063 Henry Cohn, 2026, needs more optimization.
12 292 0.430276574302 Henry Cohn, 2026, needs more optimization.
12 293 0.430777180445 Henry Cohn, 2026, needs more optimization.
12 294 0.431063166183 Henry Cohn, 2026, needs more optimization.
12 295 0.431534989927 Henry Cohn, 2026, needs more optimization.
12 296 0.431883081034 Henry Cohn, 2026, needs more optimization.
12 297 0.432324975418 Henry Cohn, 2026, needs more optimization.
12 298 0.432646995746 Henry Cohn, 2026, needs more optimization.
12 299 0.433106225107 Henry Cohn, 2026, needs more optimization.
12 300 0.433426446825 Henry Cohn, 2026, needs more optimization.
12 301 0.434535342630 Henry Cohn, 2025, needs more optimization.
12 302 0.434926474027 Henry Cohn, 2025, needs more optimization.
12 303 0.434992118487 Henry Cohn, 2025, needs more optimization.
12 304 0.435787865770 Henry Cohn, 2026, needs more optimization.
12 305 0.436091314812 Henry Cohn, 2025, needs more optimization.
12 306 0.436200612561 Henry Cohn, 2025, needs more optimization.
12 307 0.436754844887 Henry Cohn, 2025, needs more optimization.
12 308 0.436864012918 Henry Cohn, 2026, needs more optimization.
12 309 0.437471102535 Henry Cohn, 2025, needs more optimization.
12 310 0.437980374395 Henry Cohn, 2025, needs more optimization.
12 311 0.438025357358 Henry Cohn, 2025, needs more optimization.
12 312 0.438348402475 Henry Cohn, 2026, needs more optimization.
12 313 0.438801707762 Henry Cohn, 2025, needs more optimization.
12 314 0.439391293125 Henry Cohn, 2025, needs more optimization.
12 315 0.439830965838 Henry Cohn, 2025, needs more optimization.
12 316 0.440274383010 Henry Cohn, 2026, needs more optimization.
12 317 0.440347172791 Henry Cohn, 2025, needs more optimization.
12 318 0.440664248160 Henry Cohn, 2025, needs more optimization.
12 319 0.440947160843 Henry Cohn, 2025, needs more optimization.
12 320 0.441432018302 Henry Cohn, 2026, needs more optimization.
12 321 0.441715277767 Henry Cohn, 2025, needs more optimization.
12 322 0.442415599278 Henry Cohn, 2025, needs more optimization.
12 323 0.442750465096 Henry Cohn, 2025, needs more optimization.
12 324 0.443348620398 Henry Cohn, 2025, needs more optimization.
12 325 0.443421088838 Henry Cohn, 2025, needs more optimization.
12 408 0.444444444445 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
9⁢x−4
12 409 0.460317420652 Henry Cohn, 2025, needs more optimization.
12 410 0.460787274926 Henry Cohn, 2025, needs more optimization.
12 411 0.460890339256 Henry Cohn, 2025, needs more optimization.
12 412 0.460911075715 Henry Cohn, 2026, needs more optimization.
12 413 0.461342872888 Henry Cohn, 2025, needs more optimization.
12 414 0.461344809904 Henry Cohn, 2025, needs more optimization.
12 416 0.461623163776 Henry Cohn, 2026, needs more optimization.
12 417 0.462223153465 Henry Cohn, 2025, needs more optimization.
12 418 0.462255100448 Henry Cohn, 2025, needs more optimization.
12 419 0.462598213897 Henry Cohn, 2025, needs more optimization.
12 420 0.462966625030 Henry Cohn, 2026, needs more optimization.
12 422 0.463280003332 Henry Cohn, 2025, needs more optimization.
12 423 0.463392436162 Henry Cohn, 2025, needs more optimization.
12 424 0.464265187939 Henry Cohn, 2025, needs more optimization.
12 425 0.464291111787 Henry Cohn, 2025, needs more optimization.
12 426 0.464311724026 Henry Cohn, 2025, needs more optimization.
12 427 0.464333823925 Henry Cohn, 2025, needs more optimization.
12 428 0.464616426642 Henry Cohn, 2026, needs more optimization.
12 429 0.464633106668 Henry Cohn, 2025, needs more optimization.
12 430 0.464892455907 Henry Cohn, 2025, needs more optimization.
12 431 0.465132401439 Henry Cohn, 2025, needs more optimization.
12 432 0.465182768608 Henry Cohn, 2026, needs more optimization.
12 433 0.465278387386 Henry Cohn, 2025, needs more optimization.
12 434 0.465332550195 Henry Cohn, 2025, needs more optimization.
12 435 0.465390209709 Henry Cohn, 2025, needs more optimization.
12 436 0.465431254972 Henry Cohn, 2025, needs more optimization.
12 437 0.466609299805 Henry Cohn, 2025, needs more optimization.
12 438 0.466691757522 Henry Cohn, 2025, needs more optimization.
12 439 0.466712521703 Henry Cohn, 2025, needs more optimization.
12 440 0.466742768731 Henry Cohn, 2026, needs more optimization.
12 441 0.467305772666 Henry Cohn, 2025, needs more optimization.
12 442 0.467360243002 Henry Cohn, 2025, needs more optimization.
12 443 0.468001139329 Henry Cohn, 2025, needs more optimization.
12 444 0.468106256221 Henry Cohn, 2026, needs more optimization.
12 445 0.468136232732 Henry Cohn, 2025, needs more optimization.
12 446 0.468143718124 Henry Cohn, 2025, needs more optimization.
12 447 0.468255536845 Henry Cohn, 2025, needs more optimization.
12 448 0.468743091391 Henry Cohn, 2026, needs more optimization.
12 449 0.468997460954 Henry Cohn, 2025, needs more optimization.
12 450 0.469053022621 Henry Cohn, 2025, needs more optimization.
12 452 0.469731464656 Henry Cohn, 2025, needs more optimization.
12 453 0.469782575302 Henry Cohn, 2025, needs more optimization.
12 454 0.470059344042 Henry Cohn, 2025, needs more optimization.
12 455 0.470156999977 Henry Cohn, 2025, needs more optimization.
12 456 0.470337981255 Henry Cohn, 2026, needs more optimization.
12 457 0.470513260720 Henry Cohn, 2025, needs more optimization.
12 458 0.471173867096 Henry Cohn, 2025, needs more optimization.
12 459 0.471208941422 Henry Cohn, 2025, needs more optimization.
12 460 0.471276953125 Henry Cohn, 2025, needs more optimization.
12 461 0.471288301089 Henry Cohn, 2025, needs more optimization.
12 462 0.471681640270 Henry Cohn, 2025, needs more optimization.
12 463 0.471694744636 Henry Cohn, 2025, needs more optimization.
12 464 0.471725401825 Henry Cohn, 2026, needs more optimization.
12 465 0.472115369833 Henry Cohn, 2025, needs more optimization.
12 466 0.472257537181 Henry Cohn, 2025, needs more optimization.
12 467 0.472299875569 Henry Cohn, 2025, needs more optimization.
12 468 0.472594888906 Henry Cohn, 2026, needs more optimization.
12 469 0.472775609459 Henry Cohn, 2026, needs more optimization.
12 470 0.472775609464 Henry Cohn, 2025, needs more optimization.
12 471 0.472810005882 Henry Cohn, 2025, needs more optimization.
12 472 0.473173758951 Henry Cohn, 2026, needs more optimization.
12 473 0.473794201790 Henry Cohn, 2025, needs more optimization.
12 474 0.473863242716 Henry Cohn, 2025, needs more optimization.
12 475 0.473893985623 Henry Cohn, 2025, needs more optimization.
12 476 0.474320570192 Henry Cohn, 2026, needs more optimization.
12 477 0.474360536795 Henry Cohn, 2025, needs more optimization.
12 478 0.474490315931 Henry Cohn, 2025, needs more optimization.
12 480 0.474794911276 Henry Cohn, 2026, needs more optimization.
12 481 0.474879578957 Henry Cohn, 2025, needs more optimization.
12 482 0.474928668984 Henry Cohn, 2025, needs more optimization.
12 484 0.475384553366 Henry Cohn, 2025, needs more optimization.
12 485 0.475402119032 Henry Cohn, 2025, needs more optimization.
12 486 0.475751688822 Henry Cohn, 2025, needs more optimization.
12 487 0.475962860199 Henry Cohn, 2025, needs more optimization.
12 488 0.475978252243 Henry Cohn, 2025, needs more optimization.
12 489 0.476034756004 Henry Cohn, 2025, needs more optimization.
12 490 0.476066967305 Henry Cohn, 2025, needs more optimization.
12 491 0.476292844955 Henry Cohn, 2025, needs more optimization.
12 492 0.476360069412 Henry Cohn, 2026, needs more optimization.
12 493 0.476671821079 Henry Cohn, 2025, needs more optimization.
12 494 0.476699405344 Henry Cohn, 2025, needs more optimization.
12 495 0.476903460299 Henry Cohn, 2025, needs more optimization.
12 496 0.476988548405 Henry Cohn, 2026, needs more optimization.
12 497 0.477416237012 Henry Cohn, 2025, needs more optimization.
12 498 0.477438126906 Henry Cohn, 2025, needs more optimization.
12 499 0.477742523402 Henry Cohn, 2025, needs more optimization.
12 500 0.477788141354 Henry Cohn, 2026, needs more optimization.
12 501 0.477904125544 Henry Cohn, 2025, needs more optimization.
12 502 0.478134902016 Henry Cohn, 2025, needs more optimization.
12 503 0.478244559820 Henry Cohn, 2025, needs more optimization.
12 504 0.478375815422 Henry Cohn, 2026, needs more optimization.
12 505 0.479030950504 Henry Cohn, 2025, needs more optimization.
12 506 0.479034888824 Henry Cohn, 2025, needs more optimization.
12 507 0.479068778130 Henry Cohn, 2025, needs more optimization.
12 508 0.479086144303 Henry Cohn, 2025, needs more optimization.
12 510 0.479645243250 Henry Cohn, 2025, needs more optimization.
12 512 0.480566845577 Henry Cohn, 2026, needs more optimization.
12 514 0.481118705232 Henry Cohn, 2026, needs more optimization.
12 516 0.481445633633 Henry Cohn, 2026, needs more optimization.
12 517 0.481538968635 Henry Cohn, 2025, needs more optimization.
12 518 0.481559092706 Henry Cohn, 2025, needs more optimization.
12 519 0.481578191340 Henry Cohn, 2025, needs more optimization.
12 520 0.482341468928 Henry Cohn, 2026, needs more optimization.
12 521 0.482378058943 Henry Cohn, 2025, needs more optimization.
12 522 0.483196968224 Henry Cohn, 2025, needs more optimization.
12 524 0.483206384836 Henry Cohn, 2026, needs more optimization.
12 525 0.483287748702 Henry Cohn, 2025, needs more optimization.
12 527 0.483322567657 Henry Cohn, 2025, needs more optimization.
12 528 0.483329276639 Henry Cohn, 2026, needs more optimization.
12 529 0.483358658357 Henry Cohn, 2025, needs more optimization.
12 530 0.484548061479 Henry Cohn, 2025, needs more optimization.
12 532 0.484699586469 Henry Cohn, 2026, needs more optimization.
12 536 0.484768870016 Henry Cohn, 2026, needs more optimization.
12 537 0.484864119566 Henry Cohn, 2025, needs more optimization.
12 538 0.484903697721 Henry Cohn, 2025, needs more optimization.
12 539 0.484958011729 Henry Cohn, 2025, needs more optimization.
12 540 0.485896973842 Henry Cohn, 2026, needs more optimization.
12 541 0.486194227603 Henry Cohn, 2026, needs more optimization.
12 542 0.486194882963 Henry Cohn, 2026, needs more optimization.
12 543 0.486597296157 Henry Cohn, 2025, needs more optimization.
12 544 0.486636925471 Henry Cohn, 2026, needs more optimization.
12 545 0.486766063233 Henry Cohn, 2025, needs more optimization.
12 546 0.487222361280 Henry Cohn, 2025, needs more optimization.
12 547 0.487239709562 Henry Cohn, 2025, needs more optimization.
12 548 0.487250378747 Henry Cohn, 2026, needs more optimization.
12 549 0.487273017307 Henry Cohn, 2025, needs more optimization.
12 550 0.487290268268 Henry Cohn, 2025, needs more optimization.
12 552 0.487400548117 Henry Cohn, 2026, needs more optimization.
12 553 0.487478028553 Henry Cohn, 2025, needs more optimization.
12 554 0.487495550184 Henry Cohn, 2025, needs more optimization.
12 555 0.488070925645 Henry Cohn, 2025, needs more optimization.
12 556 0.488235125090 Henry Cohn, 2026, needs more optimization.
12 560 0.488333474035 Henry Cohn, 2026, needs more optimization.
12 561 0.488631669139 Henry Cohn, 2026, needs more optimization.
12 562 0.488673191441 Henry Cohn, 2026, needs more optimization.
12 563 0.488692205136 Henry Cohn, 2025, needs more optimization.
12 564 0.488697936674 Henry Cohn, 2025, needs more optimization.
12 565 0.488729497352 Henry Cohn, 2025, needs more optimization.
12 567 0.488739871268 Henry Cohn, 2025, needs more optimization.
12 569 0.488805387350 Henry Cohn, 2025, needs more optimization.
12 570 0.488818462647 Henry Cohn, 2025, needs more optimization.
12 571 0.488851947408 Henry Cohn, 2025, needs more optimization.
12 572 0.488933504580 Henry Cohn, 2026, needs more optimization.
12 573 0.488973658224 Henry Cohn, 2025, needs more optimization.
12 576 0.490363963922 Henry Cohn, 2026, needs more optimization.
12 577 0.490399992850 Henry Cohn, 2025, needs more optimization.
12 580 0.490441894573 Henry Cohn, 2025, needs more optimization.
12 581 0.490446236902 Henry Cohn, 2025, needs more optimization.
12 582 0.490487778114 Henry Cohn, 2025, needs more optimization.
12 583 0.490489697030 Henry Cohn, 2025, needs more optimization.
12 584 0.490498468096 Henry Cohn, 2025, needs more optimization.
12 585 0.490571683932 Henry Cohn, 2025, needs more optimization.
12 586 0.490675334189 Henry Cohn, 2025, needs more optimization.
12 587 0.490727775175 Henry Cohn, 2025, needs more optimization.
12 588 0.491084938853 Henry Cohn, 2026, needs more optimization.
12 590 0.492134418268 Henry Cohn, 2026, needs more optimization.
12 592 0.492137811490 Henry Cohn, 2026, needs more optimization.
12 593 0.492236784269 Henry Cohn, 2026, needs more optimization.
12 594 0.492236784461 Henry Cohn, 2025, needs more optimization.
12 595 0.492685621409 Henry Cohn, 2025, needs more optimization.
12 596 0.492773181556 Henry Cohn, 2026, needs more optimization.
12 597 0.492846250626 Henry Cohn, 2025, needs more optimization.
12 598 0.492886170361 Henry Cohn, 2025, needs more optimization.
12 599 0.494041598615 Henry Cohn, 2025, needs more optimization.
12 600 0.494044369153 Henry Cohn, 2025, needs more optimization.
12 601 0.494051376278 Henry Cohn, 2025, needs more optimization.
12 602 0.494067679491 Henry Cohn, 2025, needs more optimization.
12 603 0.494100934195 Henry Cohn, 2025, needs more optimization.
12 604 0.494121975732 Henry Cohn, 2025, needs more optimization.
12 605 0.494122442112 Henry Cohn, 2025, needs more optimization.
12 606 0.494180738460 Henry Cohn, 2025, needs more optimization.
12 607 0.494205393288 Henry Cohn, 2025, needs more optimization.
12 608 0.494260657622 Henry Cohn, 2026, needs more optimization.
12 609 0.494324177554 Henry Cohn, 2025, needs more optimization.
12 612 0.494325629276 Henry Cohn, 2025, needs more optimization.
12 613 0.494328327521 Henry Cohn, 2025, needs more optimization.
12 614 0.494645394585 Henry Cohn, 2025, needs more optimization.
12 615 0.495631117365 Henry Cohn, 2025, needs more optimization.
12 616 0.495637728423 Henry Cohn, 2025, needs more optimization.
12 619 0.495680470469 Henry Cohn, 2025, needs more optimization.
12 620 0.495681323654 Henry Cohn, 2025, needs more optimization.
12 621 0.495691130937 Henry Cohn, 2025, needs more optimization.
12 622 0.495692432016 Henry Cohn, 2025, needs more optimization.
12 623 0.495762354085 Henry Cohn, 2025, needs more optimization.
12 624 0.495762862636 Henry Cohn, 2025, needs more optimization.
12 625 0.495771634360 Henry Cohn, 2025, needs more optimization.
12 626 0.495855676060 Henry Cohn, 2025, needs more optimization.
12 628 0.495910771147 Henry Cohn, 2026, needs more optimization.
12 631 0.495949749227 Henry Cohn, 2025, needs more optimization.
12 635 0.496047783172 Henry Cohn, 2025, needs more optimization.
12 637 0.496050596998 Henry Cohn, 2025, needs more optimization.
12 638 0.496058274498 Henry Cohn, 2025, needs more optimization.
12 639 0.496064688904 Henry Cohn, 2025, needs more optimization.
12 643 0.496108643131 Henry Cohn, 2025, needs more optimization.
12 644 0.496129625185 Henry Cohn, 2025, needs more optimization.
12 645 0.496129835698 Henry Cohn, 2025, needs more optimization.
12 646 0.496131641462 Henry Cohn, 2025, needs more optimization.
12 647 0.496166216666 Henry Cohn, 2025, needs more optimization.
12 651 0.496193623279 Henry Cohn, 2025, needs more optimization.
12 653 0.496200069913 Henry Cohn, 2025, needs more optimization.
12 654 0.496204823044 Henry Cohn, 2025, needs more optimization.
12 655 0.496224318704 Henry Cohn, 2025, needs more optimization.
12 657 0.496249829119 Henry Cohn, 2025, needs more optimization.
12 658 0.496250534692 Henry Cohn, 2025, needs more optimization.
12 659 0.496251039019 Henry Cohn, 2025, needs more optimization.
12 662 0.496285882740 Henry Cohn, 2025, needs more optimization.
12 663 0.496286510903 Henry Cohn, 2025, needs more optimization.
12 665 0.496310481951 Henry Cohn, 2025, needs more optimization.
12 666 0.496347765652 Henry Cohn, 2025, needs more optimization.
12 669 0.496398243691 Henry Cohn, 2025, needs more optimization.
12 670 0.496539115043 Henry Cohn, 2025, needs more optimization.
12 671 0.496539947668 Henry Cohn, 2025, needs more optimization.
12 672 0.496554860611 Henry Cohn, 2025, needs more optimization.
12 673 0.496730130552 Henry Cohn, 2025, needs more optimization.
12 674 0.496751043235 Henry Cohn, 2025, needs more optimization.
12 675 0.496751547917 Henry Cohn, 2025, needs more optimization.
12 676 0.496753236333 Henry Cohn, 2025, needs more optimization.
12 677 0.496783428091 Henry Cohn, 2025, needs more optimization.
12 678 0.496793437471 Henry Cohn, 2025, needs more optimization.
12 679 0.496795660943 Henry Cohn, 2025, needs more optimization.
12 680 0.496798825093 Henry Cohn, 2025, needs more optimization.
12 681 0.496812843857 Henry Cohn, 2025, needs more optimization.
12 682 0.496831444646 Henry Cohn, 2025, needs more optimization.
12 683 0.496845437127 Henry Cohn, 2025, needs more optimization.
12 685 0.496851590651 Henry Cohn, 2025, needs more optimization.
12 686 0.496851824199 Henry Cohn, 2025, needs more optimization.
12 687 0.496852290623 Henry Cohn, 2025, needs more optimization.
12 688 0.496853086617 Henry Cohn, 2025, needs more optimization.
12 689 0.496854473038 Henry Cohn, 2025, needs more optimization.
12 690 0.496856167771 Henry Cohn, 2025, needs more optimization.
12 691 0.496867036500 Henry Cohn, 2025, needs more optimization.
12 692 0.496916615838 Henry Cohn, 2025, needs more optimization.
12 693 0.496939035923 Henry Cohn, 2025, needs more optimization.
12 694 0.496939223105 Henry Cohn, 2025, needs more optimization.
12 695 0.496939429832 Henry Cohn, 2025, needs more optimization.
12 696 0.496987330577 Henry Cohn, 2025, needs more optimization.
12 697 0.497010713022 Henry Cohn, 2025, needs more optimization.
12 698 0.497019280717 Henry Cohn, 2025, needs more optimization.
12 699 0.497020722181 Henry Cohn, 2025, needs more optimization.
12 700 0.497021648148 Henry Cohn, 2025, needs more optimization.
12 701 0.497047186556 Henry Cohn, 2025, needs more optimization.
12 702 0.497047692253 Henry Cohn, 2025, needs more optimization.
12 703 0.497070451054 Henry Cohn, 2025, needs more optimization.
12 704 0.497074985031 Henry Cohn, 2025, needs more optimization.
12 705 0.497081067707 Henry Cohn, 2025, needs more optimization.
12 706 0.497085905576 Henry Cohn, 2025, needs more optimization.
12 707 0.497097469933 Henry Cohn, 2025, needs more optimization.
12 708 0.497117601389 Henry Cohn, 2025, needs more optimization.
12 712 0.497131515815 Henry Cohn, 2025, needs more optimization.
12 715 0.497132897391 Henry Cohn, 2025, needs more optimization.
12 716 0.497135687687 Henry Cohn, 2025, needs more optimization.
12 717 0.497143746739 Henry Cohn, 2025, needs more optimization.
12 718 0.497173466190 Henry Cohn, 2025, needs more optimization.
12 719 0.497263801905 Henry Cohn, 2025, needs more optimization.
12 721 0.497286042343 Henry Cohn, 2025, needs more optimization.
12 722 0.497290449234 Henry Cohn, 2025, needs more optimization.
12 723 0.497312775454 Henry Cohn, 2025, needs more optimization.
12 724 0.497329208844 Henry Cohn, 2025, needs more optimization.
12 725 0.497387109813 Henry Cohn, 2025, needs more optimization.
12 726 0.497394178916 Henry Cohn, 2025, needs more optimization.
12 728 0.497399332025 Henry Cohn, 2025, needs more optimization.
12 729 0.497420674493 Henry Cohn, 2025, needs more optimization.
12 730 0.497432979281 Henry Cohn, 2025, needs more optimization.
12 731 0.497433272235 Henry Cohn, 2025, needs more optimization.
12 735 0.497433741405 Henry Cohn, 2025, needs more optimization.
12 736 0.497434002036 Henry Cohn, 2025, needs more optimization.
12 737 0.497434977729 Henry Cohn, 2025, needs more optimization.
12 739 0.497438545873 Henry Cohn, 2025, needs more optimization.
12 740 0.497468963170 Henry Cohn, 2025, needs more optimization.
12 741 0.497479222995 Henry Cohn, 2025, needs more optimization.
12 742 0.497480363182 Henry Cohn, 2025, needs more optimization.
12 743 0.497482876559 Henry Cohn, 2025, needs more optimization.
12 744 0.497514619542 Henry Cohn, 2025, needs more optimization.
12 745 0.497543875236 Henry Cohn, 2025, needs more optimization.
12 746 0.497559732219 Henry Cohn, 2025, needs more optimization.
12 747 0.497577967446 Henry Cohn, 2025, needs more optimization.
12 748 0.497599189314 Henry Cohn, 2025, needs more optimization.
12 749 0.497680832175 Henry Cohn, 2025, needs more optimization.
12 750 0.497693229718 Henry Cohn, 2025, needs more optimization.
12 751 0.497710692954 Henry Cohn, 2025, needs more optimization.
12 752 0.497711277067 Henry Cohn, 2025, needs more optimization.
12 753 0.497838301804 Henry Cohn, 2025, needs more optimization.
12 754 0.497931271352 Henry Cohn, 2026, needs more optimization.
12 755 0.498281596307 Henry Cohn, 2025, needs more optimization.
12 756 0.499541791587 H. Cohn, Y. Jiao, A. Kumar, and S. Torquato, Rigidity of spherical codes, Geom. Topol. 15 (2011), 2235–2273, doi:10.2140/gt.2011.15.2235, arXiv:1102.5060, after some further optimization.
12 840 0.5 J. Leech and N. J. A. Sloane, Sphere packings and error-correcting codes, Canadian J. Math. 23 (1971), 718–745, doi:10.4153/CJM-1971-081-3; H. Cohn, Y. Jiao, A. Kumar, and S. Torquato, Rigidity of spherical codes, Geom. Topol. 15 (2011), 2235–2273, doi:10.2140/gt.2011.15.2235, arXiv:1102.5060.
2⁢x−1
12 842 0.535503190469 Henry Cohn, 2026, needs more optimization.
12 843 0.535563528698 Henry Cohn, 2025, needs more optimization.
12 844 0.535853239784 Henry Cohn, 2026, needs more optimization.
12 845 0.535859256181 Henry Cohn, 2025, needs more optimization.
12 846 0.535864108463 Henry Cohn, 2026, needs more optimization.
12 847 0.536137465950 Henry Cohn, 2025, needs more optimization.
12 848 0.536193363348 Henry Cohn, 2026, needs more optimization.
12 849 0.536375325961 Henry Cohn, 2025, needs more optimization.
12 850 0.536420295280 Henry Cohn, 2026, needs more optimization.
12 851 0.536773139831 Henry Cohn, 2025, needs more optimization.
12 852 0.537229578938 Henry Cohn, 2026, needs more optimization.
12 853 0.537417805523 Henry Cohn, 2025, needs more optimization.
12 854 0.537422171407 Henry Cohn, 2026, needs more optimization.
12 855 0.537685598125 Henry Cohn, 2025, needs more optimization.
12 856 0.537757234848 Henry Cohn, 2026, needs more optimization.
12 857 0.537769398303 Henry Cohn, 2025, needs more optimization.
12 858 0.538135460468 Henry Cohn, 2026, needs more optimization.
12 859 0.538181862229 Henry Cohn, 2025, needs more optimization.
12 860 0.538272258203 Henry Cohn, 2026, needs more optimization.
12 861 0.538539463883 Henry Cohn, 2025, needs more optimization.
12 862 0.538787414143 Henry Cohn, 2026, needs more optimization.
12 863 0.538796771157 Henry Cohn, 2025, needs more optimization.
12 864 0.538971165052 Henry Cohn, 2026, needs more optimization.
12 866 0.539097008848 Henry Cohn, 2026, needs more optimization.
12 867 0.539420977833 Henry Cohn, 2025, needs more optimization.
12 868 0.539434575143 Henry Cohn, 2026, needs more optimization.
12 869 0.539482540123 Henry Cohn, 2025, needs more optimization.
12 870 0.539713137269 Henry Cohn, 2026, needs more optimization.
12 871 0.539940914659 Henry Cohn, 2025, needs more optimization.
12 872 0.539941280606 Henry Cohn, 2025, needs more optimization.
12 873 0.539947567768 Henry Cohn, 2025, needs more optimization.
12 874 0.539952988405 Henry Cohn, 2026, needs more optimization.
12 875 0.540538080203 Henry Cohn, 2025, needs more optimization.
12 876 0.540539657177 Henry Cohn, 2026, needs more optimization.
12 877 0.540555424019 Henry Cohn, 2025, needs more optimization.
12 878 0.540633234207 Henry Cohn, 2026, needs more optimization.
12 880 0.541219192725 Henry Cohn, 2026, needs more optimization.
12 881 0.541333676122 Henry Cohn, 2025, needs more optimization.
12 882 0.541339878624 Henry Cohn, 2026, needs more optimization.
12 883 0.541721423484 Henry Cohn, 2025, needs more optimization.
12 884 0.541997865472 Henry Cohn, 2026, needs more optimization.
12 885 0.542045952338 Henry Cohn, 2025, needs more optimization.
12 886 0.542061020507 Henry Cohn, 2026, needs more optimization.
12 887 0.542107382042 Henry Cohn, 2025, needs more optimization.
12 888 0.542472081129 Henry Cohn, 2026, needs more optimization.
12 890 0.542500247999 Henry Cohn, 2026, needs more optimization.
12 891 0.542716966071 Henry Cohn, 2025, needs more optimization.
12 892 0.542782152692 Henry Cohn, 2026, needs more optimization.
12 893 0.543207711787 Henry Cohn, 2025, needs more optimization.
12 894 0.543439354489 Henry Cohn, 2026, needs more optimization.
12 895 0.543497043904 Henry Cohn, 2025, needs more optimization.
12 896 0.543547492757 Henry Cohn, 2026, needs more optimization.
12 897 0.543893308049 Henry Cohn, 2025, needs more optimization.
12 898 0.543900823672 Henry Cohn, 2025, needs more optimization.
12 899 0.543919874490 Henry Cohn, 2025, needs more optimization.
12 900 0.543925544989 Henry Cohn, 2026, needs more optimization.
12 901 0.544322418996 Henry Cohn, 2025, needs more optimization.
12 902 0.544374835174 Henry Cohn, 2026, needs more optimization.
12 903 0.544406792234 Henry Cohn, 2025, needs more optimization.
12 904 0.544629845122 Henry Cohn, 2026, needs more optimization.
12 905 0.544667069990 Henry Cohn, 2025, needs more optimization.
12 906 0.544833542818 Henry Cohn, 2026, needs more optimization.
12 907 0.544886413273 Henry Cohn, 2025, needs more optimization.
12 908 0.545184695362 Henry Cohn, 2026, needs more optimization.
12 909 0.545209362200 Henry Cohn, 2025, needs more optimization.
12 910 0.545439672598 Henry Cohn, 2026, needs more optimization.
12 911 0.545448662084 Henry Cohn, 2025, needs more optimization.
12 912 0.545451555011 Henry Cohn, 2026, needs more optimization.
12 913 0.545474162688 Henry Cohn, 2025, needs more optimization.
12 914 0.545740004124 Henry Cohn, 2026, needs more optimization.
12 915 0.545773407652 Henry Cohn, 2025, needs more optimization.
12 916 0.546071039392 Henry Cohn, 2026, needs more optimization.
12 917 0.546077480849 Henry Cohn, 2025, needs more optimization.
12 918 0.546194488677 Henry Cohn, 2026, needs more optimization.
12 919 0.546624962329 Henry Cohn, 2025, needs more optimization.
12 920 0.546633602871 Henry Cohn, 2026, needs more optimization.
12 922 0.546646998141 Henry Cohn, 2026, needs more optimization.
12 923 0.546900657476 Henry Cohn, 2025, needs more optimization.
12 924 0.546995106625 Henry Cohn, 2026, needs more optimization.
12 925 0.547040891382 Henry Cohn, 2025, needs more optimization.
12 926 0.547177411079 Henry Cohn, 2026, needs more optimization.
12 927 0.547367953498 Henry Cohn, 2025, needs more optimization.
12 928 0.547395204939 Henry Cohn, 2026, needs more optimization.
12 929 0.547610209902 Henry Cohn, 2025, needs more optimization.
12 930 0.547618047478 Henry Cohn, 2026, needs more optimization.
12 931 0.547621635609 Henry Cohn, 2025, needs more optimization.
12 932 0.547983489649 Henry Cohn, 2026, needs more optimization.
12 933 0.548166345572 Henry Cohn, 2025, needs more optimization.
12 934 0.548174455525 Henry Cohn, 2025, needs more optimization.
12 935 0.548275056468 Henry Cohn, 2025, needs more optimization.
12 936 0.548438182116 Henry Cohn, 2026, needs more optimization.
12 937 0.548764637739 Henry Cohn, 2025, needs more optimization.
12 938 0.548955040248 Henry Cohn, 2026, needs more optimization.
12 940 0.548989417186 Henry Cohn, 2026, needs more optimization.
12 941 0.549040207156 Henry Cohn, 2025, needs more optimization.
12 942 0.549046894383 Henry Cohn, 2026, needs more optimization.
12 943 0.549450802383 Henry Cohn, 2025, needs more optimization.
12 944 0.549474745499 Henry Cohn, 2026, needs more optimization.
12 945 0.549570476958 Henry Cohn, 2025, needs more optimization.
12 946 0.549700846868 Henry Cohn, 2026, needs more optimization.
12 947 0.549729950762 Henry Cohn, 2025, needs more optimization.
12 948 0.549763578707 Henry Cohn, 2026, needs more optimization.
12 949 0.550020640206 Henry Cohn, 2025, needs more optimization.
12 950 0.550029639616 Henry Cohn, 2026, needs more optimization.
12 951 0.550085460365 Henry Cohn, 2025, needs more optimization.
12 952 0.550572418929 Henry Cohn, 2026, needs more optimization.
12 953 0.550646986647 Henry Cohn, 2025, needs more optimization.
12 954 0.550660027253 Henry Cohn, 2026, needs more optimization.
12 955 0.550675209105 Henry Cohn, 2025, needs more optimization.
12 956 0.550681015515 Henry Cohn, 2026, needs more optimization.
12 957 0.551058568831 Henry Cohn, 2025, needs more optimization.
12 958 0.551084393944 Henry Cohn, 2026, needs more optimization.
12 959 0.551092152756 Henry Cohn, 2025, needs more optimization.
12 960 0.551241431542 Henry Cohn, 2026, needs more optimization.
12 961 0.551280867106 Henry Cohn, 2025, needs more optimization.
12 962 0.551283079098 Henry Cohn, 2026, needs more optimization.
12 963 0.551568055693 Henry Cohn, 2025, needs more optimization.
12 964 0.551614803955 Henry Cohn, 2026, needs more optimization.
12 965 0.551627297606 Henry Cohn, 2025, needs more optimization.
12 966 0.551882318610 Henry Cohn, 2026, needs more optimization.
12 967 0.551889366792 Henry Cohn, 2025, needs more optimization.
12 968 0.551963913130 Henry Cohn, 2026, needs more optimization.
12 969 0.552326081648 Henry Cohn, 2025, needs more optimization.
12 970 0.552368471158 Henry Cohn, 2026, needs more optimization.
12 971 0.552378734126 Henry Cohn, 2025, needs more optimization.
12 972 0.552387393943 Henry Cohn, 2026, needs more optimization.
12 973 0.552552617952 Henry Cohn, 2025, needs more optimization.
12 974 0.552601733015 Henry Cohn, 2026, needs more optimization.
12 975 0.552630771016 Henry Cohn, 2025, needs more optimization.
12 976 0.552926775811 Henry Cohn, 2026, needs more optimization.
12 977 0.552941763697 Henry Cohn, 2025, needs more optimization.
12 978 0.553176910874 Henry Cohn, 2026, needs more optimization.
12 979 0.553188460071 Henry Cohn, 2025, needs more optimization.
12 980 0.553236896900 Henry Cohn, 2026, needs more optimization.
12 981 0.553540138207 Henry Cohn, 2025, needs more optimization.
12 982 0.553616060670 Henry Cohn, 2026, needs more optimization.
12 983 0.553797096864 Henry Cohn, 2025, needs more optimization.
12 984 0.553797650615 Henry Cohn, 2026, needs more optimization.
12 985 0.553803963339 Henry Cohn, 2025, needs more optimization.
12 986 0.554010518638 Henry Cohn, 2026, needs more optimization.
12 1024 0.555555555556 Subcode of a code of size 1144 from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−5
13 27 0.057072523783 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
1573⁢x3−169⁢x2−13⁢x+1
13 28 0.066666666667 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
15⁢x−1
13 29 0.068098609479 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
2576⁢x4−640⁢x3−184⁢x2+1
13 30 0.071714034728 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
55⁢x2+10⁢x−1
13 31 0.071714034728 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
55⁢x2+10⁢x−1
13 32 0.071714034728 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
55⁢x2+10⁢x−1
13 33 0.089954419243 Henry Cohn, 2025.
13 34 0.090095382331 Henry Cohn, 2023.
13 36 0.092610094433 H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
95⁢x2+2⁢x−1
13 37 0.111409136725 Henry Cohn, 2023.
13 38 0.112004618870 Henry Cohn, 2023.
44⁢x2+4⁢x−1
13 39 0.116893063508 Henry Cohn, 2024.
13 40 0.121353571480 Henry Cohn, 2026.
13 42 0.125 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
8⁢x−1
13 44 0.126079252818 Henry Cohn, 2025.
6095⁢x2−126⁢x−81
13 48 0.126131983623 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
47⁢x2+2⁢x−1
13 49 0.141095436175 Henry Cohn, 2025.
13 50 0.142459427551 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
13 51 0.145120831484 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
13 52 0.147159522238 Henry Cohn, 2023.
613567⁢x7+96585⁢x6−98333⁢x5−8219⁢x4+381⁢x3+539⁢x2+33⁢x−9
13 53 0.147908234060 Henry Cohn, 2024.
13 54 0.148576022240 Henry Cohn, 2025.
13 55 0.148805252884 Henry Cohn, 2024.
13 56 0.148975682089 Henry Cohn, 2023.
13 57 0.166162190421 Henry Cohn, 2024.
13 58 0.173474302723 Henry Cohn, 2023.
13 59 0.180540658957 Henry Cohn, 2024.
13 60 0.184601884691 Henry Cohn, 2025.
13 61 0.189133285981 Henry Cohn, 2026, needs more optimization.
13 62 0.189939244395 Henry Cohn, 2026.
13 63 0.193375545604 Henry Cohn, 2026.
13 64 0.194862550676 Henry Cohn, 2026, needs more optimization.
13 65 0.198938999914 Henry Cohn, 2026, needs more optimization.
13 66 0.201501645082 Henry Cohn, 2026, needs more optimization.
13 67 0.204060485677 Henry Cohn, 2026, needs more optimization.
13 68 0.207237119804 Henry Cohn, 2026, needs more optimization.
13 69 0.208427075365 Henry Cohn, 2025.
13 70 0.210762897393 Henry Cohn, 2026, needs more optimization.
13 71 0.212574330623 Henry Cohn, 2025.
13 72 0.214183844238 Henry Cohn, 2025.
13 73 0.216144703213 Henry Cohn, 2026, needs more optimization.
13 74 0.218072317405 Henry Cohn, 2026, needs more optimization.
13 75 0.219802379115 Henry Cohn, 2026, needs more optimization.
13 76 0.222090009062 Henry Cohn, 2026, needs more optimization.
13 77 0.224126205886 Henry Cohn, 2026, needs more optimization.
13 78 0.226253189158 Henry Cohn, 2026, needs more optimization.
13 79 0.228139500326 Henry Cohn, 2026, needs more optimization.
13 80 0.230720127190 Henry Cohn, 2026, needs more optimization.
13 81 0.232720216127 Henry Cohn, 2024, needs more optimization.
13 82 0.234416735243 Henry Cohn, 2026, needs more optimization.
13 83 0.236606625074 Henry Cohn, 2026, needs more optimization.
13 84 0.238167605203 Henry Cohn, 2026, needs more optimization.
13 85 0.240418979845 Henry Cohn, 2025, needs more optimization.
13 86 0.241747565738 Henry Cohn, 2026, needs more optimization.
13 87 0.243732895627 Henry Cohn, 2026, needs more optimization.
13 88 0.245463335926 Henry Cohn, 2026, needs more optimization.
13 89 0.247238849279 Henry Cohn, 2025, needs more optimization.
13 90 0.248473502762 Henry Cohn, 2026, needs more optimization.
13 104 0.25 J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment. Math. 5 (1996), 139–159, https://projecteuclid.org/euclid.em/1047565645; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
4⁢x−1
13 106 0.251575083557 Henry Cohn, 2026, needs more optimization.
13 107 0.258117042194 Henry Cohn, 2026, needs more optimization.
13 108 0.258372350014 Henry Cohn, 2026, needs more optimization.
13 109 0.259477775306 Henry Cohn, 2026, needs more optimization.
13 110 0.259624591498 Henry Cohn, 2026, needs more optimization.
13 111 0.259786920363 Henry Cohn, 2026, needs more optimization.
13 112 0.261427288349 Henry Cohn, 2026, needs more optimization.
13 113 0.263326655725 Henry Cohn, 2026, needs more optimization.
13 114 0.263627757025 Henry Cohn, 2026, needs more optimization.
13 115 0.264623765023 Henry Cohn, 2026, needs more optimization.
13 116 0.267844584869 Henry Cohn, 2026, needs more optimization.
13 117 0.270063561716 Henry Cohn, 2026, needs more optimization.
13 118 0.272924888843 Henry Cohn, 2026, needs more optimization.
13 119 0.275889133748 Henry Cohn, 2026, needs more optimization.
13 120 0.279414787328 Henry Cohn, 2026, needs more optimization.
13 121 0.280536655879 Henry Cohn, 2026, needs more optimization.
13 122 0.282199212303 Henry Cohn, 2026, needs more optimization.
13 123 0.283973352608 Henry Cohn, 2026, needs more optimization.
13 124 0.285952479277 Henry Cohn, 2026, needs more optimization.
13 125 0.287376207941 Henry Cohn, 2026, needs more optimization.
13 126 0.288695220856 Henry Cohn, 2026, needs more optimization.
13 127 0.289523518996 Henry Cohn, 2026, needs more optimization.
13 128 0.289858433697 Henry Cohn, 2026, needs more optimization.
13 129 0.291491462702 Henry Cohn, 2026, needs more optimization.
13 130 0.293843012498 Henry Cohn, 2026, needs more optimization.
13 131 0.295196826693 Henry Cohn, 2026, needs more optimization.
13 132 0.295591236152 Henry Cohn, 2026, needs more optimization.
13 133 0.296194262039 Henry Cohn, 2026, needs more optimization.
13 134 0.296743931233 Henry Cohn, 2026, needs more optimization.
13 135 0.297168693369 Henry Cohn, 2026, needs more optimization.
13 136 0.297848759780 Henry Cohn, 2026, needs more optimization.
13 137 0.298576042885 Henry Cohn, 2026, needs more optimization.
13 138 0.299035008978 Henry Cohn, 2026, needs more optimization.
13 139 0.299593760154 Henry Cohn, 2026, needs more optimization.
13 140 0.300720747547 Henry Cohn, 2026, needs more optimization.
13 141 0.301562083556 Henry Cohn, 2026, needs more optimization.
13 142 0.302631093949 Henry Cohn, 2026, needs more optimization.
13 143 0.303657149308 Henry Cohn, 2026, needs more optimization.
13 144 0.304000382163 Henry Cohn, 2026, needs more optimization.
13 145 0.305344309266 Henry Cohn, 2026, needs more optimization.
13 146 0.305525802699 Henry Cohn, 2026, needs more optimization.
13 147 0.306276192367 Henry Cohn, 2026, needs more optimization.
13 148 0.307026070388 Henry Cohn, 2026, needs more optimization.
13 149 0.307504290603 Henry Cohn, 2026, needs more optimization.
13 150 0.307817081340 Henry Cohn, 2026, needs more optimization.
13 151 0.308329513034 Henry Cohn, 2026, needs more optimization.
13 152 0.308804923456 Henry Cohn, 2026, needs more optimization.
13 153 0.309353871464 Henry Cohn, 2026, needs more optimization.
13 154 0.309802643932 Henry Cohn, 2026, needs more optimization.
13 155 0.310243359261 Henry Cohn, 2026, needs more optimization.
13 156 0.310821306924 Henry Cohn, 2026, needs more optimization.
13 157 0.311428265303 Henry Cohn, 2026, needs more optimization.
13 158 0.311968963155 Henry Cohn, 2026, needs more optimization.
13 159 0.312751890320 Henry Cohn, 2026, needs more optimization.
13 160 0.313429645346 Henry Cohn, 2026, needs more optimization.
13 161 0.314129073024 Henry Cohn, 2026, needs more optimization.
13 162 0.314412732235 Henry Cohn, 2026, needs more optimization.
13 163 0.315130081607 Henry Cohn, 2026, needs more optimization.
13 164 0.315592467627 Henry Cohn, 2026, needs more optimization.
13 165 0.316516927086 Henry Cohn, 2026, needs more optimization.
13 166 0.317269604113 Henry Cohn, 2026, needs more optimization.
13 167 0.317957744610 Henry Cohn, 2026, needs more optimization.
13 168 0.318720059283 Henry Cohn, 2026, needs more optimization.
13 169 0.319294585687 Henry Cohn, 2026, needs more optimization.
13 170 0.319599090353 Henry Cohn, 2026, needs more optimization.
13 171 0.319908425647 Henry Cohn, 2026, needs more optimization.
13 172 0.320172812712 Henry Cohn, 2026, needs more optimization.
13 173 0.320943515274 Henry Cohn, 2026, needs more optimization.
13 174 0.321508415796 Henry Cohn, 2026, needs more optimization.
13 175 0.321583050167 Henry Cohn, 2026, needs more optimization.
13 176 0.322271573336 Henry Cohn, 2026, needs more optimization.
13 177 0.322839655538 Henry Cohn, 2026, needs more optimization.
13 178 0.323108737210 Henry Cohn, 2026, needs more optimization.
13 179 0.323611453802 Henry Cohn, 2026, needs more optimization.
13 180 0.324281534377 Henry Cohn, 2026, needs more optimization.
13 181 0.324520562652 Henry Cohn, 2026, needs more optimization.
13 182 0.324886687281 Henry Cohn, 2026, needs more optimization.
13 183 0.325571477038 Henry Cohn, 2026, needs more optimization.
13 184 0.326099053768 Henry Cohn, 2026, needs more optimization.
13 185 0.326219188594 Henry Cohn, 2026, needs more optimization.
13 186 0.326481850646 Henry Cohn, 2026, needs more optimization.
13 187 0.326899840255 Henry Cohn, 2026, needs more optimization.
13 188 0.327141073373 Henry Cohn, 2026, needs more optimization.
13 189 0.327543210651 Henry Cohn, 2026, needs more optimization.
13 190 0.327611521636 Henry Cohn, 2026, needs more optimization.
13 191 0.327972386777 Henry Cohn, 2026, needs more optimization.
13 192 0.328173656428 Henry Cohn, 2026, needs more optimization.
13 193 0.328363911057 Henry Cohn, 2026, needs more optimization.
13 194 0.328431956769 Henry Cohn, 2026, needs more optimization.
13 195 0.328527706166 Henry Cohn, 2026, needs more optimization.
13 196 0.328739013237 Henry Cohn, 2026, needs more optimization.
13 197 0.328898903886 Henry Cohn, 2026, needs more optimization.
13 198 0.329119395655 Henry Cohn, 2026, needs more optimization.
13 199 0.329166236666 Henry Cohn, 2026, needs more optimization.
13 200 0.329432266216 Henry Cohn, 2026, needs more optimization.
13 201 0.329692248213 Henry Cohn, 2026, needs more optimization.
13 202 0.329895362981 Henry Cohn, 2026, needs more optimization.
13 203 0.332639607698 Henry Cohn, 2026, needs more optimization.
13 208 0.333333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−1
13 209 0.350470979699 Henry Cohn, 2025, needs more optimization.
13 210 0.351606658611 Henry Cohn, 2026, needs more optimization.
13 211 0.352321713080 Henry Cohn, 2026, needs more optimization.
13 212 0.353038683494 Henry Cohn, 2026, needs more optimization.
13 213 0.353925063398 Henry Cohn, 2026, needs more optimization.
13 214 0.354503680985 Henry Cohn, 2026, needs more optimization.
13 215 0.355465817859 Henry Cohn, 2026, needs more optimization.
13 216 0.355852066326 Henry Cohn, 2026, needs more optimization.
13 217 0.357012724305 Henry Cohn, 2026, needs more optimization.
13 218 0.357962439825 Henry Cohn, 2026, needs more optimization.
13 219 0.358139862720 Henry Cohn, 2026, needs more optimization.
13 220 0.358999772657 Henry Cohn, 2026, needs more optimization.
13 221 0.360166540430 Henry Cohn, 2026, needs more optimization.
13 222 0.360502750571 Henry Cohn, 2026, needs more optimization.
13 223 0.361611702841 Henry Cohn, 2026, needs more optimization.
13 224 0.362529805331 Henry Cohn, 2026, needs more optimization.
13 225 0.363393181712 Henry Cohn, 2026, needs more optimization.
13 226 0.364090413813 Henry Cohn, 2025, needs more optimization.
13 227 0.364776488046 Henry Cohn, 2026, needs more optimization.
13 228 0.365909317869 Henry Cohn, 2026, needs more optimization.
13 229 0.366391180286 Henry Cohn, 2026, needs more optimization.
13 230 0.367230208524 Henry Cohn, 2026, needs more optimization.
13 231 0.368177190533 Henry Cohn, 2026, needs more optimization.
13 232 0.368769845255 Henry Cohn, 2026, needs more optimization.
13 233 0.369252005489 Henry Cohn, 2026, needs more optimization.
13 234 0.370100528165 Henry Cohn, 2026, needs more optimization.
13 235 0.371116522727 Henry Cohn, 2026, needs more optimization.
13 236 0.371630810741 Henry Cohn, 2026, needs more optimization.
13 237 0.372131340429 Henry Cohn, 2026, needs more optimization.
13 238 0.373146357646 Henry Cohn, 2026, needs more optimization.
13 239 0.373752895200 Henry Cohn, 2026, needs more optimization.
13 240 0.374256685918 Henry Cohn, 2026, needs more optimization.
13 241 0.374844419047 Henry Cohn, 2026, needs more optimization.
13 242 0.375700008443 Henry Cohn, 2026, needs more optimization.
13 243 0.376317697659 Henry Cohn, 2026, needs more optimization.
13 244 0.376709523739 Henry Cohn, 2026, needs more optimization.
13 245 0.377755026511 Henry Cohn, 2026, needs more optimization.
13 246 0.378290566681 Henry Cohn, 2026, needs more optimization.
13 247 0.378891825919 Henry Cohn, 2026, needs more optimization.
13 248 0.379384317543 Henry Cohn, 2026, needs more optimization.
13 249 0.380098148874 Henry Cohn, 2026, needs more optimization.
13 250 0.380786089999 Henry Cohn, 2026, needs more optimization.
13 251 0.381491823702 Henry Cohn, 2026, needs more optimization.
13 252 0.381963272515 Henry Cohn, 2024, needs more optimization.
13 253 0.382864339660 Henry Cohn, 2026, needs more optimization.
13 254 0.383277389646 Henry Cohn, 2026, needs more optimization.
13 255 0.384387375524 Henry Cohn, 2026, needs more optimization.
13 306 0.384615384616 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
13⁢x−5
13 313 0.384615384616 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
13⁢x−5
13 336 0.4 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
5⁢x−2
13 337 0.417891478892 Henry Cohn, 2025, needs more optimization.
13 338 0.418441080028 Henry Cohn, 2025, needs more optimization.
13 339 0.418737825194 Henry Cohn, 2025, needs more optimization.
13 340 0.418875769127 Henry Cohn, 2025, needs more optimization.
13 341 0.419419034847 Henry Cohn, 2025, needs more optimization.
13 342 0.420049026491 Henry Cohn, 2025, needs more optimization.
13 343 0.420070225222 Henry Cohn, 2025, needs more optimization.
13 344 0.420389870109 Henry Cohn, 2026, needs more optimization.
13 345 0.420581365637 Henry Cohn, 2025, needs more optimization.
13 346 0.420704154424 Henry Cohn, 2025, needs more optimization.
13 347 0.421102107698 Henry Cohn, 2025, needs more optimization.
13 348 0.421543178185 Henry Cohn, 2026, needs more optimization.
13 349 0.421907425104 Henry Cohn, 2025, needs more optimization.
13 350 0.422008380280 Henry Cohn, 2025, needs more optimization.
13 351 0.422575939533 Henry Cohn, 2025, needs more optimization.
13 352 0.422858125025 Henry Cohn, 2026, needs more optimization.
13 353 0.423230257051 Henry Cohn, 2025, needs more optimization.
13 354 0.423743822805 Henry Cohn, 2025, needs more optimization.
13 355 0.424058260598 Henry Cohn, 2025, needs more optimization.
13 356 0.424139492882 Henry Cohn, 2026, needs more optimization.
13 357 0.424432715559 Henry Cohn, 2025, needs more optimization.
13 358 0.424991924513 Henry Cohn, 2025, needs more optimization.
13 359 0.425356584705 Henry Cohn, 2025, needs more optimization.
13 360 0.425473600075 Henry Cohn, 2026, needs more optimization.
13 361 0.426053892700 Henry Cohn, 2025, needs more optimization.
13 363 0.426403543342 Henry Cohn, 2025, needs more optimization.
13 364 0.426672402227 Henry Cohn, 2026, needs more optimization.
13 365 0.427322675493 Henry Cohn, 2025, needs more optimization.
13 416 0.428571428572 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−3
13 492 0.428571428572 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
7⁢x−3
13 578 0.454545454546 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
11⁢x−5
13 579 0.465672455233 Henry Cohn, 2025, needs more optimization.
13 580 0.465789763135 Henry Cohn, 2026, needs more optimization.
13 581 0.465955526650 Henry Cohn, 2025, needs more optimization.
13 582 0.466342901539 Henry Cohn, 2026, needs more optimization.
13 584 0.466530373366 Henry Cohn, 2026, needs more optimization.
13 585 0.466832748141 Henry Cohn, 2025, needs more optimization.
13 586 0.467549101040 Henry Cohn, 2025, needs more optimization.
13 588 0.467574032999 Henry Cohn, 2026, needs more optimization.
13 592 0.467711301366 Henry Cohn, 2026, needs more optimization.
13 596 0.467769086876 Henry Cohn, 2026, needs more optimization.
13 597 0.470122617375 Henry Cohn, 2025, needs more optimization.
13 598 0.470135903308 Henry Cohn, 2025, needs more optimization.
13 599 0.470605232123 Henry Cohn, 2026, needs more optimization.
13 600 0.470770397994 Henry Cohn, 2026, needs more optimization.
13 601 0.471026039091 Henry Cohn, 2025, needs more optimization.
13 602 0.472796352342 Henry Cohn, 2025, needs more optimization.
13 603 0.473262426000 Henry Cohn, 2025, needs more optimization.
13 604 0.473278998215 Henry Cohn, 2026, needs more optimization.
13 605 0.473324558816 Henry Cohn, 2025, needs more optimization.
13 606 0.473522802978 Henry Cohn, 2025, needs more optimization.
13 608 0.473604551063 Henry Cohn, 2026, needs more optimization.
13 609 0.473627679841 Henry Cohn, 2025, needs more optimization.
13 610 0.473665833105 Henry Cohn, 2025, needs more optimization.
13 611 0.473739534858 Henry Cohn, 2025, needs more optimization.
13 612 0.473965827048 Henry Cohn, 2026, needs more optimization.
13 613 0.474406686573 Henry Cohn, 2025, needs more optimization.
13 614 0.474476481362 Henry Cohn, 2025, needs more optimization.
13 615 0.474494086062 Henry Cohn, 2025, needs more optimization.
13 616 0.474905852839 Henry Cohn, 2026, needs more optimization.
13 617 0.474918963482 Henry Cohn, 2025, needs more optimization.
13 618 0.474967584162 Henry Cohn, 2025, needs more optimization.
13 619 0.475383863231 Henry Cohn, 2025, needs more optimization.
13 620 0.475415073774 Henry Cohn, 2026, needs more optimization.
13 621 0.475458135871 Henry Cohn, 2025, needs more optimization.
13 622 0.475534670877 Henry Cohn, 2025, needs more optimization.
13 623 0.475564411116 Henry Cohn, 2025, needs more optimization.
13 624 0.475772458391 Henry Cohn, 2025, needs more optimization.
13 625 0.476105619632 Henry Cohn, 2025, needs more optimization.
13 626 0.476125930108 Henry Cohn, 2025, needs more optimization.
13 627 0.476133672282 Henry Cohn, 2025, needs more optimization.
13 628 0.476274391676 Henry Cohn, 2026, needs more optimization.
13 629 0.476497765410 Henry Cohn, 2025, needs more optimization.
13 630 0.476682055609 Henry Cohn, 2025, needs more optimization.
13 632 0.476753462685 Henry Cohn, 2026, needs more optimization.
13 633 0.476779642724 Henry Cohn, 2025, needs more optimization.
13 634 0.476863611299 Henry Cohn, 2025, needs more optimization.
13 635 0.477164338899 Henry Cohn, 2025, needs more optimization.
13 636 0.477264749703 Henry Cohn, 2026, needs more optimization.
13 637 0.477285852944 Henry Cohn, 2025, needs more optimization.
13 638 0.477612729804 Henry Cohn, 2025, needs more optimization.
13 639 0.477701773044 Henry Cohn, 2025, needs more optimization.
13 640 0.477865043264 Henry Cohn, 2026, needs more optimization.
13 641 0.477876519895 Henry Cohn, 2025, needs more optimization.
13 642 0.477880331706 Henry Cohn, 2025, needs more optimization.
13 644 0.478030845536 Henry Cohn, 2026, needs more optimization.
13 645 0.478368394521 Henry Cohn, 2025, needs more optimization.
13 646 0.478412887584 Henry Cohn, 2025, needs more optimization.
13 647 0.478492404615 Henry Cohn, 2025, needs more optimization.
13 648 0.478503335799 Henry Cohn, 2026, needs more optimization.
13 649 0.478509908716 Henry Cohn, 2025, needs more optimization.
13 650 0.478832290317 Henry Cohn, 2025, needs more optimization.
13 651 0.478838229297 Henry Cohn, 2025, needs more optimization.
13 652 0.478856464367 Henry Cohn, 2026, needs more optimization.
13 653 0.479050421989 Henry Cohn, 2025, needs more optimization.
13 654 0.479071333898 Henry Cohn, 2025, needs more optimization.
13 655 0.479603675125 Henry Cohn, 2025, needs more optimization.
13 656 0.479613974451 Henry Cohn, 2026, needs more optimization.
13 657 0.479687023902 Henry Cohn, 2025, needs more optimization.
13 658 0.479704383217 Henry Cohn, 2025, needs more optimization.
13 659 0.479730979245 Henry Cohn, 2025, needs more optimization.
13 660 0.480347440524 Henry Cohn, 2026, needs more optimization.
13 661 0.480364890268 Henry Cohn, 2025, needs more optimization.
13 662 0.480375210672 Henry Cohn, 2025, needs more optimization.
13 663 0.480405879307 Henry Cohn, 2025, needs more optimization.
13 664 0.480454278236 Henry Cohn, 2026, needs more optimization.
13 665 0.480771700158 Henry Cohn, 2025, needs more optimization.
13 666 0.480815251640 Henry Cohn, 2025, needs more optimization.
13 667 0.480821848300 Henry Cohn, 2025, needs more optimization.
13 668 0.480831213922 Henry Cohn, 2026, needs more optimization.
13 670 0.480891611906 Henry Cohn, 2025, needs more optimization.
13 672 0.481273438735 Henry Cohn, 2025, needs more optimization.
13 673 0.481283021102 Henry Cohn, 2025, needs more optimization.
13 674 0.481286722824 Henry Cohn, 2025, needs more optimization.
13 675 0.481644119395 Henry Cohn, 2025, needs more optimization.
13 676 0.481799113049 Henry Cohn, 2026, needs more optimization.
13 677 0.481830390467 Henry Cohn, 2025, needs more optimization.
13 678 0.481839212161 Henry Cohn, 2025, needs more optimization.
13 679 0.482152300430 Henry Cohn, 2025, needs more optimization.
13 680 0.482154819163 Henry Cohn, 2026, needs more optimization.
13 681 0.482169815140 Henry Cohn, 2025, needs more optimization.
13 682 0.482446092429 Henry Cohn, 2026, needs more optimization.
13 684 0.482480693519 Henry Cohn, 2026, needs more optimization.
13 685 0.482658262037 Henry Cohn, 2025, needs more optimization.
13 686 0.482707808246 Henry Cohn, 2026, needs more optimization.
13 687 0.482727338345 Henry Cohn, 2025, needs more optimization.
13 688 0.482904616258 Henry Cohn, 2026, needs more optimization.
13 690 0.482936949385 Henry Cohn, 2026, needs more optimization.
13 691 0.483009366512 Henry Cohn, 2025, needs more optimization.
13 692 0.483662493176 Henry Cohn, 2026, needs more optimization.
13 693 0.483691006742 Henry Cohn, 2025, needs more optimization.
13 694 0.483724892704 Henry Cohn, 2026, needs more optimization.
13 695 0.483792803740 Henry Cohn, 2025, needs more optimization.
13 696 0.483798522832 Henry Cohn, 2026, needs more optimization.
13 697 0.483911175969 Henry Cohn, 2025, needs more optimization.
13 698 0.484135521202 Henry Cohn, 2026, needs more optimization.
13 699 0.484204749320 Henry Cohn, 2025, needs more optimization.
13 700 0.484227609270 Henry Cohn, 2026, needs more optimization.
13 701 0.484248420249 Henry Cohn, 2025, needs more optimization.
13 702 0.484285803164 Henry Cohn, 2026, needs more optimization.
13 703 0.484305418348 Henry Cohn, 2025, needs more optimization.
13 704 0.484321914872 Henry Cohn, 2026, needs more optimization.
13 705 0.484447011111 Henry Cohn, 2025, needs more optimization.
13 706 0.484672767524 Henry Cohn, 2026, needs more optimization.
13 707 0.484760353386 Henry Cohn, 2025, needs more optimization.
13 708 0.484898375649 Henry Cohn, 2026, needs more optimization.
13 710 0.484933992513 Henry Cohn, 2026, needs more optimization.
13 712 0.484987569503 Henry Cohn, 2026, needs more optimization.
13 713 0.485222047626 Henry Cohn, 2025, needs more optimization.
13 714 0.485281723031 Henry Cohn, 2026, needs more optimization.
13 715 0.485403154566 Henry Cohn, 2025, needs more optimization.
13 716 0.485451228042 Henry Cohn, 2026, needs more optimization.
13 717 0.485463210063 Henry Cohn, 2025, needs more optimization.
13 718 0.485465400333 Henry Cohn, 2026, needs more optimization.
13 719 0.485468162774 Henry Cohn, 2025, needs more optimization.
13 720 0.485489349759 Henry Cohn, 2026, needs more optimization.
13 721 0.485591204459 Henry Cohn, 2025, needs more optimization.
13 722 0.485623534964 Henry Cohn, 2026, needs more optimization.
13 723 0.485669629147 Henry Cohn, 2025, needs more optimization.
13 724 0.486214777807 Henry Cohn, 2026, needs more optimization.
13 726 0.486262022021 Henry Cohn, 2026, needs more optimization.
13 728 0.486315569030 Henry Cohn, 2026, needs more optimization.
13 729 0.486343174788 Henry Cohn, 2025, needs more optimization.
13 730 0.486344751192 Henry Cohn, 2026, needs more optimization.
13 732 0.486398271121 Henry Cohn, 2026, needs more optimization.
13 733 0.486424756451 Henry Cohn, 2025, needs more optimization.
13 734 0.486470573631 Henry Cohn, 2026, needs more optimization.
13 735 0.486528687498 Henry Cohn, 2025, needs more optimization.
13 736 0.486541827480 Henry Cohn, 2026, needs more optimization.
13 737 0.486610781541 Henry Cohn, 2025, needs more optimization.
13 738 0.486625678301 Henry Cohn, 2026, needs more optimization.
13 739 0.486674807439 Henry Cohn, 2025, needs more optimization.
13 740 0.486747665413 Henry Cohn, 2026, needs more optimization.
13 741 0.486774481368 Henry Cohn, 2025, needs more optimization.
13 742 0.486782295403 Henry Cohn, 2026, needs more optimization.
13 744 0.486809080246 Henry Cohn, 2026, needs more optimization.
13 745 0.486832029598 Henry Cohn, 2025, needs more optimization.
13 746 0.486859781045 Henry Cohn, 2026, needs more optimization.
13 747 0.486995072672 Henry Cohn, 2025, needs more optimization.
13 748 0.487288300144 Henry Cohn, 2026, needs more optimization.
13 749 0.487297499593 Henry Cohn, 2025, needs more optimization.
13 750 0.487325957512 Henry Cohn, 2026, needs more optimization.
13 751 0.487380839577 Henry Cohn, 2025, needs more optimization.
13 752 0.487382031309 Henry Cohn, 2026, needs more optimization.
13 754 0.487395788319 Henry Cohn, 2026, needs more optimization.
13 755 0.487502436563 Henry Cohn, 2025, needs more optimization.
13 756 0.487564772802 Henry Cohn, 2026, needs more optimization.
13 757 0.487742083046 Henry Cohn, 2026, needs more optimization.
13 758 0.487778612423 Henry Cohn, 2026, needs more optimization.
13 1024 0.5 Subcode of a kissing configuration from J. Leech and N. J. A. Sloane, Sphere packings and error-correcting codes, Canadian J. Math. 23 (1971), 718–745, doi:10.4153/CJM-1971-081-3.
2⁢x−1
14 29 0.053426987342 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
2016⁢x3−196⁢x2−14⁢x+1
14 30 0.0625 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
16⁢x−1
14 31 0.067582771839 H. Cohn, Small spherical and projective codes, data set, updated 2025, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
14 32 0.071430901841 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
14 33 0.071678780313 Henry Cohn, 2025.
14 34 0.071706747799 Henry Cohn, 2025.
14 36 0.080003299193 Henry Cohn, 2023.
2156⁢x2+140⁢x−25
14 37 0.087892856445 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
14 38 0.092604004700 Henry Cohn, 2025.
14 39 0.094407135777 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
14 42 0.1 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
10⁢x−1
14 43 0.112894921393 Henry Cohn, 2025.
14 45 0.112912613537 Henry Cohn, 2023.
167⁢x2−10⁢x−1
14 46 0.114212424977 Henry Cohn, 2024.
14 47 0.114744370065 Henry Cohn, 2026.
14 48 0.114785923011 Henry Cohn, 2023.
1988352⁢x8+1963008⁢x7−108672⁢x6−513152⁢x5−92592⁢x4+19616⁢x3+5240⁢x2+72⁢x−81
14 49 0.125031168050 Henry Cohn, 2025.
14 50 0.126129943174 Henry Cohn, 2025.
14 52 0.126131983623 Henry Cohn, 2023.
47⁢x2+2⁢x−1
14 53 0.127206627186 Henry Cohn, 2025.
14 54 0.135105967369 Henry Cohn, 2024.
14 55 0.136745922263 Henry Cohn, 2023.
14 56 0.139995758129 Henry Cohn, 2024.
14 57 0.142106619426 Henry Cohn, 2025.
14 64 0.142857142858 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
7⁢x−1
14 65 0.165287555076 Henry Cohn, 2024.
25600⁢x4−5616⁢x3−2736⁢x2+81
14 70 0.166666666667 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
6⁢x−1
14 71 0.177427267176 Henry Cohn, 2024.
196⁢x4−56⁢x3−28⁢x2+1
14 72 0.180989672412 Henry Cohn, 2026.
14 73 0.184685922154 Henry Cohn, 2026, needs more optimization.
14 75 0.185110498567 Henry Cohn, 2026, needs more optimization.
14 76 0.189888419708 Henry Cohn, 2026, needs more optimization.
14 77 0.192044340104 Henry Cohn, 2026, needs more optimization.
14 78 0.192681299289 Henry Cohn, 2026, needs more optimization.
14 79 0.194319485351 Henry Cohn, 2026, needs more optimization.
14 80 0.195567913043 Henry Cohn, 2026, needs more optimization.
14 81 0.198109586451 Henry Cohn, 2026, needs more optimization.
14 83 0.198343910648 Henry Cohn, 2026, needs more optimization.
14 84 0.198352242654 Henry Cohn, 2026, needs more optimization.
14 85 0.198385543226 Henry Cohn, 2026, needs more optimization.
14 86 0.198455824071 Henry Cohn, 2026, needs more optimization.
14 87 0.198500556742 Henry Cohn, 2026, needs more optimization.
14 88 0.198573230999 Henry Cohn, 2026, needs more optimization.
14 89 0.198677263321 Henry Cohn, 2026, needs more optimization.
14 90 0.198771953024 Henry Cohn, 2026, needs more optimization.
14 91 0.198843416031 Henry Cohn, 2026, needs more optimization.
14 92 0.208457898342 Henry Cohn, 2026, needs more optimization.
14 93 0.212930218599 Henry Cohn, 2026, needs more optimization.
14 94 0.213929020886 Henry Cohn, 2026, needs more optimization.
14 95 0.217145618324 Henry Cohn, 2026, needs more optimization.
14 96 0.217581736905 Henry Cohn, 2026, needs more optimization.
14 97 0.217987275841 Henry Cohn, 2026, needs more optimization.
14 98 0.219808790643 Henry Cohn, 2026, needs more optimization.
14 99 0.222120043573 Henry Cohn, 2026, needs more optimization.
14 100 0.223728320054 Henry Cohn, 2026, needs more optimization.
14 101 0.225620988107 Henry Cohn, 2026, needs more optimization.
14 102 0.228335097166 Henry Cohn, 2026, needs more optimization.
14 112 0.229910395528 Henry Cohn, 2026, needs more optimization.
14 113 0.234903720985 Henry Cohn, 2026, needs more optimization.
14 114 0.237369497279 Henry Cohn, 2026, needs more optimization.
14 115 0.239325281760 Henry Cohn, 2026, needs more optimization.
14 116 0.240935156065 Henry Cohn, 2026, needs more optimization.
14 117 0.242371582782 Henry Cohn, 2026, needs more optimization.
14 118 0.244115274965 Henry Cohn, 2026, needs more optimization.
14 119 0.244941008540 Henry Cohn, 2026, needs more optimization.
14 120 0.246542776600 Henry Cohn, 2026, needs more optimization.
14 121 0.247804837635 Henry Cohn, 2026, needs more optimization.
14 122 0.249222342079 Henry Cohn, 2026, needs more optimization.
14 123 0.250379704445 Henry Cohn, 2026, needs more optimization.
14 124 0.251250704298 Henry Cohn, 2026, needs more optimization.
14 125 0.252289325846 Henry Cohn, 2026, needs more optimization.
14 126 0.253313260997 Henry Cohn, 2026, needs more optimization.
14 127 0.254061789773 Henry Cohn, 2026, needs more optimization.
14 128 0.254664010994 Henry Cohn, 2026, needs more optimization.
14 129 0.255355902029 Henry Cohn, 2026, needs more optimization.
14 130 0.256043761691 Henry Cohn, 2026, needs more optimization.
14 131 0.259574413142 Henry Cohn, 2026, needs more optimization.
14 132 0.261696058723 Henry Cohn, 2026, needs more optimization.
14 133 0.262945587611 Henry Cohn, 2026, needs more optimization.
14 134 0.264542191163 Henry Cohn, 2026, needs more optimization.
14 135 0.265754813181 Henry Cohn, 2026, needs more optimization.
14 136 0.266955244988 Henry Cohn, 2026, needs more optimization.
14 137 0.268453936435 Henry Cohn, 2026, needs more optimization.
14 138 0.269360778127 Henry Cohn, 2026, needs more optimization.
14 139 0.269360821523 Henry Cohn, 2026, needs more optimization.
14 140 0.269363487463 Henry Cohn, 2026, needs more optimization.
14 141 0.269364653598 Henry Cohn, 2026, needs more optimization.
14 142 0.269374502335 Henry Cohn, 2026, needs more optimization.
14 143 0.269376035730 Henry Cohn, 2026, needs more optimization.
14 144 0.269378796345 Henry Cohn, 2026, needs more optimization.
14 145 0.269385310491 Henry Cohn, 2026, needs more optimization.
14 146 0.269391870899 Henry Cohn, 2026, needs more optimization.
14 147 0.269406679942 Henry Cohn, 2026, needs more optimization.
14 148 0.269436221839 Henry Cohn, 2026, needs more optimization.
14 149 0.269471439877 Henry Cohn, 2026, needs more optimization.
14 150 0.269516324115 Henry Cohn, 2026, needs more optimization.
14 152 0.269752269749 Henry Cohn, 2026, needs more optimization.
14 153 0.273185531224 Henry Cohn, 2026, needs more optimization.
14 154 0.273861278753 Henry Cohn, 2026.
40⁢x2−3
14 156 0.283473354757 Henry Cohn, 2024.
112⁢x2−9
14 157 0.291885744635 Henry Cohn, 2026, needs more optimization.
14 158 0.292313560776 Henry Cohn, 2026, needs more optimization.
14 159 0.293004245086 Henry Cohn, 2026, needs more optimization.
14 160 0.293162619310 Henry Cohn, 2026, needs more optimization.
14 161 0.293549215092 Henry Cohn, 2026, needs more optimization.
14 162 0.293988182622 Henry Cohn, 2026, needs more optimization.
14 163 0.295028878850 Henry Cohn, 2026, needs more optimization.
14 164 0.295133717897 Henry Cohn, 2026, needs more optimization.
14 165 0.295273167176 Henry Cohn, 2026, needs more optimization.
14 166 0.296155191022 Henry Cohn, 2026, needs more optimization.
14 167 0.296761213381 Henry Cohn, 2026, needs more optimization.
14 168 0.297490707135 Henry Cohn, 2026, needs more optimization.
14 169 0.298400715609 Henry Cohn, 2026, needs more optimization.
14 170 0.298465389592 Henry Cohn, 2026, needs more optimization.
14 171 0.299464104905 Henry Cohn, 2026, needs more optimization.
14 172 0.299739266301 Henry Cohn, 2026, needs more optimization.
14 173 0.300155751293 Henry Cohn, 2026, needs more optimization.
14 174 0.300831450912 Henry Cohn, 2026, needs more optimization.
14 175 0.302015327062 Henry Cohn, 2026, needs more optimization.
14 176 0.303303391718 Henry Cohn, 2026, needs more optimization.
14 177 0.303334854461 Henry Cohn, 2026, needs more optimization.
14 178 0.303608718119 Henry Cohn, 2026, needs more optimization.
14 179 0.304176086793 Henry Cohn, 2026, needs more optimization.
14 180 0.304571820240 Henry Cohn, 2026, needs more optimization.
14 181 0.304631631929 Henry Cohn, 2026, needs more optimization.
14 182 0.305192282576 Henry Cohn, 2026, needs more optimization.
14 183 0.305666184939 Henry Cohn, 2026, needs more optimization.
14 184 0.306391461325 Henry Cohn, 2026, needs more optimization.
14 185 0.307118198138 Henry Cohn, 2026, needs more optimization.
14 186 0.307303438684 Henry Cohn, 2026, needs more optimization.
14 187 0.307653978923 Henry Cohn, 2026, needs more optimization.
14 188 0.308322525936 Henry Cohn, 2026, needs more optimization.
14 189 0.308663546186 Henry Cohn, 2026, needs more optimization.
14 190 0.309360390961 Henry Cohn, 2026, needs more optimization.
14 197 0.309624611734 Henry Cohn, 2026, needs more optimization.
14 198 0.310241667907 Henry Cohn, 2026, needs more optimization.
14 199 0.310771455822 Henry Cohn, 2026, needs more optimization.
14 200 0.311252797643 Henry Cohn, 2026, needs more optimization.
14 201 0.312523234365 Henry Cohn, 2026, needs more optimization.
14 202 0.313578633458 Henry Cohn, 2026, needs more optimization.
14 203 0.314998211666 Henry Cohn, 2026, needs more optimization.
14 204 0.315825283579 Henry Cohn, 2026, needs more optimization.
14 205 0.316805640246 Henry Cohn, 2026, needs more optimization.
14 206 0.317333666271 Henry Cohn, 2026, needs more optimization.
14 207 0.317863760607 Henry Cohn, 2026, needs more optimization.
14 210 0.318181818182 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
22⁢x−7
14 211 0.325237190232 Henry Cohn, 2026, needs more optimization.
14 213 0.325296125129 Henry Cohn, 2026, needs more optimization.
14 214 0.325539772727 Henry Cohn, 2026, needs more optimization.
14 215 0.325608137456 Henry Cohn, 2026, needs more optimization.
14 216 0.325622468768 Henry Cohn, 2026, needs more optimization.
14 217 0.325726341030 Henry Cohn, 2026, needs more optimization.
14 218 0.325827122751 Henry Cohn, 2026, needs more optimization.
14 219 0.325883792645 Henry Cohn, 2026, needs more optimization.
14 220 0.326116896181 Henry Cohn, 2026, needs more optimization.
14 221 0.326918787317 Henry Cohn, 2026, needs more optimization.
14 222 0.326986105033 Henry Cohn, 2026, needs more optimization.
14 223 0.327071206132 Henry Cohn, 2026, needs more optimization.
14 224 0.327203925862 Henry Cohn, 2026, needs more optimization.
14 225 0.327570966121 Henry Cohn, 2026, needs more optimization.
14 226 0.327594408743 Henry Cohn, 2026, needs more optimization.
14 227 0.328079378435 Henry Cohn, 2026, needs more optimization.
14 228 0.328434662335 Henry Cohn, 2026, needs more optimization.
14 229 0.328589621977 Henry Cohn, 2026, needs more optimization.
14 230 0.328969557149 Henry Cohn, 2026, needs more optimization.
14 240 0.333333333334 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
3⁢x−1
14 252 0.333333333334 C. Ma, T. T. Zhaowei, P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
3⁢x−1
14 254 0.348228091414 Henry Cohn, 2026, needs more optimization.
14 255 0.349093446821 Henry Cohn, 2026, needs more optimization.
14 256 0.349099317126 Henry Cohn, 2026, needs more optimization.
14 257 0.349146546868 Henry Cohn, 2026, needs more optimization.
14 258 0.349429822708 Henry Cohn, 2026, needs more optimization.
14 259 0.349609234861 Henry Cohn, 2026, needs more optimization.
14 260 0.349697776015 Henry Cohn, 2026, needs more optimization.
14 261 0.350017604419 Henry Cohn, 2026, needs more optimization.
14 262 0.350101683506 Henry Cohn, 2026, needs more optimization.
14 263 0.350138048688 Henry Cohn, 2026, needs more optimization.
14 264 0.351678846576 Henry Cohn, 2026, needs more optimization.
14 265 0.351707619775 Henry Cohn, 2026, needs more optimization.
14 266 0.351731136767 Henry Cohn, 2026, needs more optimization.
14 267 0.351757022154 Henry Cohn, 2026, needs more optimization.
14 268 0.351839126165 Henry Cohn, 2026, needs more optimization.
14 269 0.352076312504 Henry Cohn, 2026, needs more optimization.
14 270 0.352265343868 Henry Cohn, 2026, needs more optimization.
14 272 0.352365891070 Henry Cohn, 2026, needs more optimization.
14 273 0.352694160387 Henry Cohn, 2026, needs more optimization.
14 274 0.352877344477 Henry Cohn, 2026, needs more optimization.
14 276 0.353102325072 Henry Cohn, 2026, needs more optimization.
14 277 0.353234413318 Henry Cohn, 2026, needs more optimization.
14 278 0.353906292766 Henry Cohn, 2026, needs more optimization.
14 279 0.353919363230 Henry Cohn, 2026, needs more optimization.
14 281 0.354089834130 Henry Cohn, 2026, needs more optimization.
14 282 0.354222114054 Henry Cohn, 2026, needs more optimization.
14 283 0.354275349136 Henry Cohn, 2026, needs more optimization.
14 284 0.354437016909 Henry Cohn, 2026, needs more optimization.
14 285 0.354629938736 Henry Cohn, 2026, needs more optimization.
14 286 0.354659214912 Henry Cohn, 2026, needs more optimization.
14 287 0.354678598213 Henry Cohn, 2026, needs more optimization.
14 288 0.354698270662 Henry Cohn, 2026, needs more optimization.
14 289 0.354709739187 Henry Cohn, 2026, needs more optimization.
14 290 0.354720959468 Henry Cohn, 2026, needs more optimization.
14 291 0.354837309695 Henry Cohn, 2026, needs more optimization.
14 292 0.355114823627 Henry Cohn, 2026, needs more optimization.
14 293 0.355270184236 Henry Cohn, 2026, needs more optimization.
14 294 0.355368455636 Henry Cohn, 2026, needs more optimization.
14 295 0.355369705102 Henry Cohn, 2026, needs more optimization.
14 296 0.355372895389 Henry Cohn, 2026, needs more optimization.
14 300 0.355377450170 Henry Cohn, 2026, needs more optimization.
14 304 0.355592458266 Henry Cohn, 2026, needs more optimization.
14 306 0.355595026220 Henry Cohn, 2026, needs more optimization.
14 307 0.355596245382 Henry Cohn, 2026, needs more optimization.
14 310 0.355596344014 Henry Cohn, 2026, needs more optimization.
14 317 0.355596615854 Henry Cohn, 2026, needs more optimization.
14 318 0.355598619036 Henry Cohn, 2026, needs more optimization.
14 320 0.355598733128 Henry Cohn, 2026, needs more optimization.
14 321 0.355603161787 Henry Cohn, 2026, needs more optimization.
14 322 0.355607105198 Henry Cohn, 2026, needs more optimization.
14 324 0.355612603920 Henry Cohn, 2026, needs more optimization.
14 325 0.355616443419 Henry Cohn, 2026, needs more optimization.
14 327 0.355620633097 Henry Cohn, 2026, needs more optimization.
14 328 0.355620672265 Henry Cohn, 2026, needs more optimization.
14 329 0.355623601673 Henry Cohn, 2026, needs more optimization.
14 330 0.355626910653 Henry Cohn, 2026, needs more optimization.
14 331 0.355647861564 Henry Cohn, 2026, needs more optimization.
14 332 0.355662272317 Henry Cohn, 2026, needs more optimization.
14 333 0.356491665492 Henry Cohn, 2026, needs more optimization.
14 335 0.356523872657 Henry Cohn, 2026, needs more optimization.
14 336 0.356530903868 Henry Cohn, 2026, needs more optimization.
14 337 0.356729335160 Henry Cohn, 2026, needs more optimization.
14 338 0.356783585587 Henry Cohn, 2026, needs more optimization.
14 339 0.358507191076 Henry Cohn, 2026, needs more optimization.
14 340 0.359862871314 Henry Cohn, 2026, needs more optimization.
14 341 0.360721335636 Henry Cohn, 2026, needs more optimization.
14 343 0.367824826104 Henry Cohn, 2026, needs more optimization.
14 344 0.368268128693 Henry Cohn, 2026, needs more optimization.
14 345 0.368689125461 Henry Cohn, 2026, needs more optimization.
14 348 0.368808647722 Henry Cohn, 2026, needs more optimization.
14 350 0.369160447936 Henry Cohn, 2026, needs more optimization.
14 351 0.369397909736 Henry Cohn, 2026, needs more optimization.
14 352 0.370682642393 Henry Cohn, 2026, needs more optimization.
14 364 0.378350393632 Henry Cohn, 2026, needs more optimization.
14 365 0.379505399137 Henry Cohn, 2026, needs more optimization.
14 368 0.379518558288 Henry Cohn, 2026, needs more optimization.
14 369 0.379588636561 Henry Cohn, 2026, needs more optimization.
14 370 0.379617042154 Henry Cohn, 2026, needs more optimization.
14 372 0.379671965923 Henry Cohn, 2026, needs more optimization.
14 376 0.379736746844 Henry Cohn, 2026, needs more optimization.
14 380 0.382596035899 Henry Cohn, 2026, needs more optimization.
14 384 0.382719113175 Henry Cohn, 2026, needs more optimization.
14 386 0.383144972193 Henry Cohn, 2026, needs more optimization.
14 466 0.4 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
14 492 0.4 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
14 600 0.428571428572 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
7⁢x−3
14 601 0.429784647320 Henry Cohn, 2026, needs more optimization.
14 602 0.430091119011 Henry Cohn, 2025, needs more optimization.
14 603 0.430255500551 Henry Cohn, 2025, needs more optimization.
14 604 0.430605377846 Henry Cohn, 2026, needs more optimization.
14 605 0.431095901490 Henry Cohn, 2025, needs more optimization.
14 606 0.431192286990 Henry Cohn, 2025, needs more optimization.
14 607 0.431236397848 Henry Cohn, 2025, needs more optimization.
14 608 0.431365482112 Henry Cohn, 2026, needs more optimization.
14 609 0.431552382817 Henry Cohn, 2025, needs more optimization.
14 610 0.431669143554 Henry Cohn, 2026, needs more optimization.
14 611 0.431687232253 Henry Cohn, 2025, needs more optimization.
14 612 0.432192772355 Henry Cohn, 2026, needs more optimization.
14 614 0.432432822618 Henry Cohn, 2025, needs more optimization.
14 616 0.432898752936 Henry Cohn, 2026, needs more optimization.
14 618 0.433020999307 Henry Cohn, 2025, needs more optimization.
14 620 0.433039391703 Henry Cohn, 2026, needs more optimization.
14 621 0.433126440825 Henry Cohn, 2025, needs more optimization.
14 624 0.433145754655 Henry Cohn, 2026, needs more optimization.
14 625 0.433243537011 Henry Cohn, 2025, needs more optimization.
14 626 0.433282562279 Henry Cohn, 2025, needs more optimization.
14 627 0.433311094830 Henry Cohn, 2025, needs more optimization.
14 628 0.433563716319 Henry Cohn, 2026, needs more optimization.
14 630 0.433668758998 Henry Cohn, 2025, needs more optimization.
14 632 0.433688204409 Henry Cohn, 2026, needs more optimization.
14 634 0.433779719638 Henry Cohn, 2025, needs more optimization.
14 636 0.433832897674 Henry Cohn, 2026, needs more optimization.
14 637 0.433915481050 Henry Cohn, 2025, needs more optimization.
14 638 0.433959497508 Henry Cohn, 2025, needs more optimization.
14 639 0.433963466338 Henry Cohn, 2025, needs more optimization.
14 640 0.434234535028 Henry Cohn, 2026, needs more optimization.
14 641 0.434243537160 Henry Cohn, 2025, needs more optimization.
14 642 0.434246541036 Henry Cohn, 2025, needs more optimization.
14 644 0.451502692839 Henry Cohn, 2026, needs more optimization.
14 646 0.451526932364 Henry Cohn, 2025, needs more optimization.
14 648 0.451555266873 Henry Cohn, 2026, needs more optimization.
14 649 0.451565788068 Henry Cohn, 2025, needs more optimization.
14 652 0.451683741627 Henry Cohn, 2026, needs more optimization.
14 654 0.451699556322 Henry Cohn, 2025, needs more optimization.
14 656 0.451788208457 Henry Cohn, 2026, needs more optimization.
14 660 0.452033205431 Henry Cohn, 2026, needs more optimization.
14 896 0.454545454546 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11⁢x−5
14 897 0.454721351053 Henry Cohn, 2026, needs more optimization.
14 898 0.454820209793 Henry Cohn, 2026, needs more optimization.
14 899 0.454870853392 Henry Cohn, 2026, needs more optimization.
14 900 0.454887890162 Henry Cohn, 2026, needs more optimization.
14 901 0.454931070240 Henry Cohn, 2026, needs more optimization.
14 902 0.454952665399 Henry Cohn, 2026, needs more optimization.
14 903 0.454999625082 Henry Cohn, 2026, needs more optimization.
14 904 0.455055416212 Henry Cohn, 2026, needs more optimization.
14 906 0.455098117000 Henry Cohn, 2026, needs more optimization.
14 908 0.455121613794 Henry Cohn, 2026, needs more optimization.
14 910 0.455159335404 Henry Cohn, 2026, needs more optimization.
14 912 0.455187226387 Henry Cohn, 2026, needs more optimization.
14 914 0.455210036234 Henry Cohn, 2026, needs more optimization.
14 916 0.455249105039 Henry Cohn, 2026, needs more optimization.
14 917 0.455285139780 Henry Cohn, 2025, needs more optimization.
14 918 0.455286091523 Henry Cohn, 2026, needs more optimization.
14 920 0.455326887293 Henry Cohn, 2026, needs more optimization.
14 922 0.455345687557 Henry Cohn, 2026, needs more optimization.
14 923 0.455372029754 Henry Cohn, 2025, needs more optimization.
14 924 0.492313427682 Henry Cohn, 2026, needs more optimization.
14 925 0.492327194287 Henry Cohn, 2025, needs more optimization.
14 926 0.492439035611 Henry Cohn, 2026, needs more optimization.
14 927 0.492666262172 Henry Cohn, 2025, needs more optimization.
14 928 0.492676366579 Henry Cohn, 2026, needs more optimization.
14 929 0.492692208983 Henry Cohn, 2025, needs more optimization.
14 930 0.492973056405 Henry Cohn, 2026, needs more optimization.
14 931 0.493017067245 Henry Cohn, 2025, needs more optimization.
14 932 0.493028038540 Henry Cohn, 2026, needs more optimization.
14 933 0.493099194502 Henry Cohn, 2025, needs more optimization.
14 934 0.493420721055 Henry Cohn, 2026, needs more optimization.
14 935 0.493436866895 Henry Cohn, 2025, needs more optimization.
14 936 0.493474884160 Henry Cohn, 2026, needs more optimization.
14 937 0.493641027705 Henry Cohn, 2025, needs more optimization.
14 938 0.493689294396 Henry Cohn, 2026, needs more optimization.
14 939 0.493706887962 Henry Cohn, 2025, needs more optimization.
14 940 0.493962683689 Henry Cohn, 2026, needs more optimization.
14 941 0.493974355695 Henry Cohn, 2025, needs more optimization.
14 942 0.494138863563 Henry Cohn, 2026, needs more optimization.
14 943 0.494147583322 Henry Cohn, 2025, needs more optimization.
14 944 0.494409198434 Henry Cohn, 2026, needs more optimization.
14 945 0.494441938719 Henry Cohn, 2025, needs more optimization.
14 946 0.494456422769 Henry Cohn, 2025, needs more optimization.
14 947 0.494688575887 Henry Cohn, 2025, needs more optimization.
14 948 0.494703928253 Henry Cohn, 2026, needs more optimization.
14 949 0.494749973807 Henry Cohn, 2025, needs more optimization.
14 950 0.495008690645 Henry Cohn, 2026, needs more optimization.
14 951 0.495023039759 Henry Cohn, 2025, needs more optimization.
14 952 0.495023447217 Henry Cohn, 2026, needs more optimization.
14 953 0.495031085664 Henry Cohn, 2025, needs more optimization.
14 954 0.495147935962 Henry Cohn, 2025, needs more optimization.
14 956 0.495168651929 Henry Cohn, 2026, needs more optimization.
14 957 0.495376527378 Henry Cohn, 2025, needs more optimization.
14 958 0.495377637529 Henry Cohn, 2026, needs more optimization.
14 960 0.495657184832 Henry Cohn, 2026, needs more optimization.
14 961 0.495765560894 Henry Cohn, 2025, needs more optimization.
14 962 0.496049763619 Henry Cohn, 2026, needs more optimization.
14 963 0.496056693148 Henry Cohn, 2025, needs more optimization.
14 964 0.496130338879 Henry Cohn, 2026, needs more optimization.
14 965 0.496348709997 Henry Cohn, 2025, needs more optimization.
14 966 0.496367793629 Henry Cohn, 2026, needs more optimization.
14 967 0.496389317457 Henry Cohn, 2025, needs more optimization.
14 968 0.496389619657 Henry Cohn, 2026, needs more optimization.
14 970 0.496654723830 Henry Cohn, 2026, needs more optimization.
14 971 0.496922774268 Henry Cohn, 2025, needs more optimization.
14 972 0.496975899538 Henry Cohn, 2026, needs more optimization.
14 973 0.497000563595 Henry Cohn, 2025, needs more optimization.
14 974 0.497065736068 Henry Cohn, 2026, needs more optimization.
14 975 0.497289348022 Henry Cohn, 2025, needs more optimization.
14 976 0.497304672293 Henry Cohn, 2026, needs more optimization.
14 977 0.497364578162 Henry Cohn, 2025, needs more optimization.
14 978 0.497601982326 Henry Cohn, 2026, needs more optimization.
14 979 0.497654773739 Henry Cohn, 2025, needs more optimization.
14 980 0.497677114082 Henry Cohn, 2026, needs more optimization.
14 981 0.497751573565 Henry Cohn, 2025, needs more optimization.
14 982 0.497985418945 Henry Cohn, 2026, needs more optimization.
14 983 0.498011822506 Henry Cohn, 2025, needs more optimization.
14 984 0.498020685452 Henry Cohn, 2026, needs more optimization.
14 985 0.498029179824 Henry Cohn, 2025, needs more optimization.
14 986 0.498290396229 Henry Cohn, 2026, needs more optimization.
14 987 0.498476341963 Henry Cohn, 2025, needs more optimization.
14 988 0.498541834310 Henry Cohn, 2026, needs more optimization.
14 989 0.498578439165 Henry Cohn, 2025, needs more optimization.
14 990 0.498756442434 Henry Cohn, 2026, needs more optimization.
14 1024 0.5 Subcode of a kissing configuration from J. Leech and N. J. A. Sloane, Sphere packings and error-correcting codes, Canadian J. Math. 23 (1971), 718–745, doi:10.4153/CJM-1971-081-3.
2⁢x−1
15 31 0.050237120373 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
2535⁢x3−225⁢x2−15⁢x+1
15 32 0.058900808489 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
15 33 0.062706770083 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
15 34 0.066570393658 Henry Cohn, 2025.
15 35 0.070509992992 Henry Cohn, 2023.
15 36 0.070779968044 Henry Cohn, 2023.
5937⁢x4+412⁢x3−202⁢x2−4⁢x+1
15 37 0.078785666352 Henry Cohn, 2025.
15 38 0.079970260232 Henry Cohn, 2026.
15 39 0.082681671944 Henry Cohn, 2023.
347087⁢x8+1080416⁢x7+305012⁢x6+3648⁢x5−20054⁢x4−160⁢x3+276⁢x2−1
15 40 0.086159367074 Henry Cohn, 2023.
15 41 0.093058708471 Henry Cohn, 2026.
15 42 0.096809796022 Henry Cohn, 2023.
15 43 0.099863843733 Henry Cohn, 2025.
15 44 0.099976426707 Henry Cohn, 2025.
15 45 0.105767188891 Henry Cohn, 2023.
15 46 0.110795000982 Henry Cohn, 2025.
15 47 0.111165028345 Henry Cohn, 2026.
15 48 0.112519700675 Henry Cohn, 2026.
15 52 0.112912613537 Henry Cohn, 2025.
167⁢x2−10⁢x−1
15 57 0.115470053838 Henry Cohn, 2024.
75⁢x2−1
15 58 0.119568772343 Henry Cohn, 2025.
15 61 0.128458591981 Henry Cohn, 2025.
263⁢x2−26⁢x−1
15 62 0.129619175385 Henry Cohn, 2025, needs more optimization.
15 63 0.129675303921 Henry Cohn, 2026, needs more optimization.
15 64 0.129676245976 Henry Cohn, 2025, needs more optimization.
15 65 0.129676247045 Henry Cohn, 2026, needs more optimization.
15 66 0.142849849465 Henry Cohn, 2025.
15 67 0.144353409494 Henry Cohn, 2023.
15 68 0.146740451793 Henry Cohn, 2026.
15 69 0.160033734974 Henry Cohn, 2024.
15 70 0.160964563056 Henry Cohn, 2024.
15 71 0.166512948843 Henry Cohn, 2025.
15 72 0.166656830714 Henry Cohn, 2026, needs more optimization.
15 73 0.166704540358 Henry Cohn, 2026, needs more optimization.
15 92 0.168685175113 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
47⁢x2−2⁢x−1
15 93 0.169916676995 Henry Cohn, 2025.
169⁢x4−56⁢x3−30⁢x2+1
15 94 0.186858652300 Henry Cohn, 2026, needs more optimization.
15 95 0.187145879513 Henry Cohn, 2026, needs more optimization.
15 96 0.188201821306 Henry Cohn, 2026, needs more optimization.
15 99 0.188682094168 Henry Cohn, 2026, needs more optimization.
15 100 0.189764266343 Henry Cohn, 2026, needs more optimization.
15 128 0.2 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
5⁢x−1
15 129 0.209693852061 Henry Cohn, 2026, needs more optimization.
15 130 0.216744767943 Henry Cohn, 2026, needs more optimization.
15 131 0.219841453500 Henry Cohn, 2026, needs more optimization.
15 132 0.221699429606 Henry Cohn, 2026, needs more optimization.
15 133 0.223240086287 Henry Cohn, 2026, needs more optimization.
15 134 0.226013010231 Henry Cohn, 2026, needs more optimization.
15 135 0.226122593087 Henry Cohn, 2026, needs more optimization.
15 136 0.226153149527 Henry Cohn, 2026, needs more optimization.
15 137 0.226888915734 Henry Cohn, 2026, needs more optimization.
15 142 0.227160244716 Henry Cohn, 2026, needs more optimization.
15 143 0.232905189967 Henry Cohn, 2026, needs more optimization.
15 144 0.236485146657 Henry Cohn, 2026, needs more optimization.
15 145 0.238711916037 Henry Cohn, 2026, needs more optimization.
15 146 0.238721231839 Henry Cohn, 2026, needs more optimization.
15 147 0.238762616069 Henry Cohn, 2026, needs more optimization.
15 150 0.239559057179 Henry Cohn, 2026, needs more optimization.
15 151 0.244766676204 Henry Cohn, 2026, needs more optimization.
15 152 0.245248898373 Henry Cohn, 2026, needs more optimization.
15 153 0.245510293392 Henry Cohn, 2026, needs more optimization.
15 154 0.249413184522 Henry Cohn, 2026, needs more optimization.
15 156 0.25 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
4⁢x−1
15 157 0.251119981016 Henry Cohn, 2026, needs more optimization.
15 158 0.254970525135 Henry Cohn, 2026, needs more optimization.
15 159 0.261528226184 Henry Cohn, 2026, needs more optimization.
15 160 0.264450322591 Henry Cohn, 2026, needs more optimization.
15 161 0.265389041845 Henry Cohn, 2026, needs more optimization.
15 162 0.266601509974 Henry Cohn, 2026, needs more optimization.
15 163 0.267642717982 Henry Cohn, 2026, needs more optimization.
15 164 0.268013083767 Henry Cohn, 2026, needs more optimization.
15 165 0.268800204545 Henry Cohn, 2026, needs more optimization.
15 166 0.269139489004 Henry Cohn, 2026, needs more optimization.
15 167 0.269280737260 Henry Cohn, 2026, needs more optimization.
15 168 0.269496728441 Henry Cohn, 2026, needs more optimization.
15 169 0.269641042563 Henry Cohn, 2026, needs more optimization.
15 170 0.269752866225 Henry Cohn, 2026, needs more optimization.
15 171 0.269814089735 Henry Cohn, 2026, needs more optimization.
15 172 0.269850002255 Henry Cohn, 2026, needs more optimization.
15 173 0.269926266637 Henry Cohn, 2026, needs more optimization.
15 174 0.270214442214 Henry Cohn, 2026, needs more optimization.
15 175 0.270369885635 Henry Cohn, 2026, needs more optimization.
15 176 0.270472512377 Henry Cohn, 2026, needs more optimization.
15 177 0.270564586034 Henry Cohn, 2026, needs more optimization.
15 178 0.270603933063 Henry Cohn, 2026, needs more optimization.
15 179 0.270722449942 Henry Cohn, 2026, needs more optimization.
15 180 0.270853599818 Henry Cohn, 2026, needs more optimization.
15 181 0.270938799034 Henry Cohn, 2026, needs more optimization.
15 182 0.271104974687 Henry Cohn, 2026, needs more optimization.
15 183 0.271196576854 Henry Cohn, 2026, needs more optimization.
15 184 0.271314803183 Henry Cohn, 2026, needs more optimization.
15 185 0.271406759686 Henry Cohn, 2026, needs more optimization.
15 186 0.271477923533 Henry Cohn, 2026, needs more optimization.
15 187 0.271544899159 Henry Cohn, 2026, needs more optimization.
15 188 0.271591282404 Henry Cohn, 2026, needs more optimization.
15 189 0.271681301540 Henry Cohn, 2026, needs more optimization.
15 190 0.271716503410 Henry Cohn, 2026, needs more optimization.
15 191 0.271914022957 Henry Cohn, 2026, needs more optimization.
15 192 0.272059922222 Henry Cohn, 2026, needs more optimization.
15 193 0.272209409089 Henry Cohn, 2026, needs more optimization.
15 194 0.272499671956 Henry Cohn, 2026, needs more optimization.
15 195 0.272578233537 Henry Cohn, 2026, needs more optimization.
15 196 0.272632639160 Henry Cohn, 2026, needs more optimization.
15 210 0.272675720243 Henry Cohn, 2026, needs more optimization.
15 211 0.272697193144 Henry Cohn, 2026, needs more optimization.
15 212 0.272714899761 Henry Cohn, 2026, needs more optimization.
15 213 0.272757899467 Henry Cohn, 2026, needs more optimization.
15 214 0.272777338001 Henry Cohn, 2026, needs more optimization.
15 215 0.272812470333 Henry Cohn, 2026, needs more optimization.
15 216 0.272875302011 Henry Cohn, 2026, needs more optimization.
15 217 0.272911621594 Henry Cohn, 2026, needs more optimization.
15 218 0.273001493872 Henry Cohn, 2026, needs more optimization.
15 219 0.273085903378 Henry Cohn, 2026, needs more optimization.
15 220 0.273152783280 Henry Cohn, 2026, needs more optimization.
15 240 0.304347826087 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
23⁢x−7
15 256 0.304347826087 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
23⁢x−7
15 257 0.304907913664 Henry Cohn, 2026, needs more optimization.
15 258 0.305116738245 Henry Cohn, 2026, needs more optimization.
15 259 0.306602551551 Henry Cohn, 2026, needs more optimization.
15 263 0.309536394471 Henry Cohn, 2026, needs more optimization.
15 264 0.310172221735 Henry Cohn, 2026, needs more optimization.
15 265 0.321180427261 Henry Cohn, 2026, needs more optimization.
15 266 0.321432314178 Henry Cohn, 2026, needs more optimization.
15 267 0.321760306814 Henry Cohn, 2026, needs more optimization.
15 268 0.322013813399 Henry Cohn, 2026, needs more optimization.
15 269 0.322229695435 Henry Cohn, 2026, needs more optimization.
15 320 0.333333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−1
15 321 0.339370412683 Henry Cohn, 2026, needs more optimization.
15 322 0.340377089292 Henry Cohn, 2026, needs more optimization.
15 323 0.353686979309 Henry Cohn, 2026, needs more optimization.
15 324 0.354487292678 Henry Cohn, 2026, needs more optimization.
15 325 0.354517119657 Henry Cohn, 2026, needs more optimization.
15 326 0.354530545782 Henry Cohn, 2026, needs more optimization.
15 328 0.354566984239 Henry Cohn, 2026, needs more optimization.
15 329 0.354604194827 Henry Cohn, 2026, needs more optimization.
15 330 0.354632594790 Henry Cohn, 2026, needs more optimization.
15 331 0.354649136399 Henry Cohn, 2026, needs more optimization.
15 332 0.354679346979 Henry Cohn, 2026, needs more optimization.
15 333 0.354719040551 Henry Cohn, 2026, needs more optimization.
15 336 0.354741888911 Henry Cohn, 2026, needs more optimization.
15 337 0.354826816308 Henry Cohn, 2026, needs more optimization.
15 338 0.355259895838 Henry Cohn, 2026, needs more optimization.
15 340 0.355260132304 Henry Cohn, 2026, needs more optimization.
15 341 0.355290388162 Henry Cohn, 2026, needs more optimization.
15 342 0.355290659496 Henry Cohn, 2026, needs more optimization.
15 344 0.355309909755 Henry Cohn, 2026, needs more optimization.
15 346 0.355346604838 Henry Cohn, 2026, needs more optimization.
15 347 0.355351162570 Henry Cohn, 2026, needs more optimization.
15 348 0.355353509195 Henry Cohn, 2026, needs more optimization.
15 352 0.355493648494 Henry Cohn, 2026, needs more optimization.
15 353 0.355525152696 Henry Cohn, 2026, needs more optimization.
15 356 0.355527321103 Henry Cohn, 2026, needs more optimization.
15 358 0.355550069943 Henry Cohn, 2026, needs more optimization.
15 359 0.355600275452 Henry Cohn, 2026, needs more optimization.
15 360 0.355602110975 Henry Cohn, 2026, needs more optimization.
15 361 0.355610820517 Henry Cohn, 2026, needs more optimization.
15 362 0.355618827570 Henry Cohn, 2026, needs more optimization.
15 363 0.355650983568 Henry Cohn, 2026, needs more optimization.
15 364 0.355659351583 Henry Cohn, 2026, needs more optimization.
15 365 0.355680342401 Henry Cohn, 2026, needs more optimization.
15 366 0.355710147631 Henry Cohn, 2026, needs more optimization.
15 367 0.355716028864 Henry Cohn, 2026, needs more optimization.
15 368 0.355726879627 Henry Cohn, 2026, needs more optimization.
15 369 0.355772992600 Henry Cohn, 2026, needs more optimization.
15 370 0.355849158957 Henry Cohn, 2026, needs more optimization.
15 371 0.355865550171 Henry Cohn, 2026, needs more optimization.
15 372 0.355878923713 Henry Cohn, 2026, needs more optimization.
15 373 0.356896924733 Henry Cohn, 2026, needs more optimization.
15 374 0.357213563423 Henry Cohn, 2026, needs more optimization.
15 375 0.357327127633 Henry Cohn, 2026, needs more optimization.
15 376 0.359572438356 Henry Cohn, 2026, needs more optimization.
15 377 0.359692245708 Henry Cohn, 2026, needs more optimization.
15 378 0.359761801743 Henry Cohn, 2026, needs more optimization.
15 380 0.360767005407 Henry Cohn, 2026, needs more optimization.
15 381 0.361027875254 Henry Cohn, 2026, needs more optimization.
15 382 0.361107627164 Henry Cohn, 2026, needs more optimization.
15 383 0.361793558670 Henry Cohn, 2026, needs more optimization.
15 384 0.362898403048 Henry Cohn, 2026, needs more optimization.
15 385 0.363400396726 Henry Cohn, 2026, needs more optimization.
15 386 0.364162589879 Henry Cohn, 2026, needs more optimization.
15 388 0.365849255935 Henry Cohn, 2026, needs more optimization.
15 389 0.384420108204 Henry Cohn, 2025, needs more optimization.
15 390 0.384918541898 Henry Cohn, 2025, needs more optimization.
15 391 0.385074975412 Henry Cohn, 2026, needs more optimization.
15 392 0.385592066086 Henry Cohn, 2026, needs more optimization.
15 393 0.385697573797 Henry Cohn, 2025, needs more optimization.
15 394 0.385984331138 Henry Cohn, 2025, needs more optimization.
15 395 0.386225226866 Henry Cohn, 2025, needs more optimization.
15 396 0.386591348150 Henry Cohn, 2026, needs more optimization.
15 397 0.387116282587 Henry Cohn, 2025, needs more optimization.
15 398 0.387172791615 Henry Cohn, 2025, needs more optimization.
15 399 0.387606636643 Henry Cohn, 2025, needs more optimization.
15 400 0.387878096356 Henry Cohn, 2026, needs more optimization.
15 401 0.387891088276 Henry Cohn, 2026, needs more optimization.
15 402 0.388339855674 Henry Cohn, 2025, needs more optimization.
15 403 0.388757758623 Henry Cohn, 2025, needs more optimization.
15 404 0.388759488830 Henry Cohn, 2026, needs more optimization.
15 405 0.388931907229 Henry Cohn, 2026, needs more optimization.
15 406 0.389252002498 Henry Cohn, 2026, needs more optimization.
15 407 0.389817861267 Henry Cohn, 2025, needs more optimization.
15 408 0.389821569051 Henry Cohn, 2026, needs more optimization.
15 409 0.390093941582 Henry Cohn, 2025, needs more optimization.
15 410 0.390221832356 Henry Cohn, 2025, needs more optimization.
15 411 0.390425306732 Henry Cohn, 2025, needs more optimization.
15 412 0.390743554804 Henry Cohn, 2026, needs more optimization.
15 413 0.391420636625 Henry Cohn, 2025, needs more optimization.
15 414 0.391448228914 Henry Cohn, 2026, needs more optimization.
15 415 0.391481727130 Henry Cohn, 2026, needs more optimization.
15 416 0.391883380232 Henry Cohn, 2026, needs more optimization.
15 420 0.391884257975 Henry Cohn, 2026, needs more optimization.
15 428 0.391884808657 Henry Cohn, 2026, needs more optimization.
15 432 0.391885825686 Henry Cohn, 2026, needs more optimization.
15 433 0.391904247888 Henry Cohn, 2025, needs more optimization.
15 436 0.391906778679 Henry Cohn, 2026, needs more optimization.
15 440 0.391910082861 Henry Cohn, 2026, needs more optimization.
15 442 0.391915123600 Henry Cohn, 2025, needs more optimization.
15 443 0.391960592920 Henry Cohn, 2026, needs more optimization.
15 444 0.391965011895 Henry Cohn, 2026, needs more optimization.
15 448 0.391969898330 Henry Cohn, 2026, needs more optimization.
15 449 0.391974552177 Henry Cohn, 2026, needs more optimization.
15 451 0.391982342905 Henry Cohn, 2026, needs more optimization.
15 452 0.391997881677 Henry Cohn, 2026, needs more optimization.
15 453 0.392010208274 Henry Cohn, 2026, needs more optimization.
15 456 0.392017018253 Henry Cohn, 2026, needs more optimization.
15 458 0.392020856406 Henry Cohn, 2026, needs more optimization.
15 459 0.392023857282 Henry Cohn, 2026, needs more optimization.
15 460 0.392040567096 Henry Cohn, 2026, needs more optimization.
15 462 0.392041602720 Henry Cohn, 2026, needs more optimization.
15 464 0.392065844463 Henry Cohn, 2026, needs more optimization.
15 465 0.392134371424 Henry Cohn, 2026, needs more optimization.
15 466 0.392165142082 Henry Cohn, 2026, needs more optimization.
15 468 0.392664769104 Henry Cohn, 2026, needs more optimization.
15 470 0.392707676584 Henry Cohn, 2026, needs more optimization.
15 471 0.392759590039 Henry Cohn, 2026, needs more optimization.
15 472 0.392830095296 Henry Cohn, 2026, needs more optimization.
15 473 0.392851877606 Henry Cohn, 2026, needs more optimization.
15 474 0.393154346772 Henry Cohn, 2026, needs more optimization.
15 475 0.393157298956 Henry Cohn, 2026, needs more optimization.
15 476 0.393197710439 Henry Cohn, 2026, needs more optimization.
15 477 0.393294692202 Henry Cohn, 2026, needs more optimization.
15 478 0.393443890839 Henry Cohn, 2026, needs more optimization.
15 479 0.393468087110 Henry Cohn, 2026, needs more optimization.
15 480 0.393710218068 Henry Cohn, 2026, needs more optimization.
15 481 0.393785259773 Henry Cohn, 2026, needs more optimization.
15 484 0.393967039706 Henry Cohn, 2026, needs more optimization.
15 485 0.394156496480 Henry Cohn, 2026, needs more optimization.
15 486 0.394316441201 Henry Cohn, 2026, needs more optimization.
15 672 0.4 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
15 688 0.4 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
15 990 0.428571428572 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
7⁢x−3
15 994 0.454647357440 Henry Cohn, 2026, needs more optimization.
15 998 0.454656625504 Henry Cohn, 2026, needs more optimization.
15 999 0.454677607826 Henry Cohn, 2025, needs more optimization.
15 1001 0.454678212405 Henry Cohn, 2025, needs more optimization.
15 1002 0.454734240452 Henry Cohn, 2026, needs more optimization.
15 1004 0.454780412996 Henry Cohn, 2026, needs more optimization.
15 1006 0.454789504648 Henry Cohn, 2026, needs more optimization.
15 1008 0.454800278479 Henry Cohn, 2026, needs more optimization.
15 1010 0.454831522563 Henry Cohn, 2026, needs more optimization.
15 1011 0.454837749616 Henry Cohn, 2025, needs more optimization.
15 1012 0.454838359249 Henry Cohn, 2026, needs more optimization.
15 1013 0.454845479817 Henry Cohn, 2025, needs more optimization.
15 1014 0.454896648547 Henry Cohn, 2026, needs more optimization.
15 1018 0.454913946680 Henry Cohn, 2026, needs more optimization.
15 1020 0.454926265220 Henry Cohn, 2026, needs more optimization.
15 1022 0.454944092149 Henry Cohn, 2026, needs more optimization.
15 1023 0.454961053016 Henry Cohn, 2026, needs more optimization.
15 1024 0.454977519070 Henry Cohn, 2026, needs more optimization.
16 33 0.047421028894 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3136⁢x3−256⁢x2−16⁢x+1
16 34 0.055555555556 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
18⁢x−1
16 36 0.056002309435 Henry Cohn, 2023.
176⁢x2+8⁢x−1
16 38 0.065186804094 Henry Cohn, 2023.
7312⁢x4+864⁢x3−200⁢x2−8⁢x+1
16 39 0.074285234713 Henry Cohn, 2025.
16 40 0.077433436468 Henry Cohn, 2024.
16 41 0.078328485376 Henry Cohn, 2023.
16 42 0.085112299907 Henry Cohn, 2025.
16 44 0.085376587737 Henry Cohn, 2023.
512⁢x2−32⁢x−1
16 45 0.090651346396 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
16 46 0.095440859515 Henry Cohn, 2025.
16 47 0.097443031003 Henry Cohn, 2025.
16 48 0.098771717854 Henry Cohn, 2023.
143⁢x2−4⁢x−1
16 49 0.105254154031 Henry Cohn, 2025.
16 50 0.108974791166 Henry Cohn, 2026.
16 51 0.111198306019 Henry Cohn, 2025.
16 52 0.111567586034 Henry Cohn, 2026.
16 53 0.112902421936 Henry Cohn, 2025.
16 54 0.112907159448 Henry Cohn, 2025.
16 55 0.113137877868 Henry Cohn, 2026.
16 58 0.113835450316 Henry Cohn, 2026.
288⁢x2−24⁢x−1
16 59 0.115469803431 Henry Cohn, 2023, needs more optimization.
16 60 0.115470801109 Henry Cohn, 2026, needs more optimization.
16 61 0.119371454413 Henry Cohn, 2025.
16 62 0.125768177302 Henry Cohn, 2025.
16 74 0.127284656799 Henry Cohn, 2023.
156⁢x2−12⁢x−1
16 75 0.142415975160 Henry Cohn, 2025, needs more optimization.
16 76 0.157616857308 Henry Cohn, 2025.
16 77 0.161334829806 Henry Cohn, 2026, needs more optimization.
16 78 0.164417462768 Henry Cohn, 2026, needs more optimization.
16 79 0.167447335055 Henry Cohn, 2026, needs more optimization.
16 80 0.167572018919 Henry Cohn, 2026, needs more optimization.
16 81 0.167749834182 Henry Cohn, 2026, needs more optimization.
16 82 0.167923286051 Henry Cohn, 2026, needs more optimization.
16 83 0.168279307188 Henry Cohn, 2026, needs more optimization.
16 84 0.168596157094 Henry Cohn, 2026, needs more optimization.
16 85 0.168666428099 Henry Cohn, 2025, needs more optimization.
16 88 0.168668499420 Henry Cohn, 2025, needs more optimization.
16 92 0.168684604646 Henry Cohn, 2025, needs more optimization.
16 94 0.168684943107 Henry Cohn, 2025, needs more optimization.
16 96 0.168685705337 Henry Cohn, 2026, needs more optimization.
16 97 0.169880759680 Henry Cohn, 2026, needs more optimization.
16 102 0.170753175474 Henry Cohn, 2026.
128⁢x2−16⁢x−1
16 103 0.174178397918 Henry Cohn, 2026, needs more optimization.
16 104 0.179379121655 Henry Cohn, 2026, needs more optimization.
16 105 0.183420437163 Henry Cohn, 2026, needs more optimization.
16 106 0.185897329735 Henry Cohn, 2025, needs more optimization.
16 107 0.188035141309 Henry Cohn, 2026, needs more optimization.
16 108 0.191388162639 Henry Cohn, 2026, needs more optimization.
16 116 0.192450089730 Henry Cohn, 2026.
27⁢x2−1
16 117 0.198855471670 Henry Cohn, 2026, needs more optimization.
16 118 0.198870263710 Henry Cohn, 2026, needs more optimization.
16 119 0.198900209819 Henry Cohn, 2026, needs more optimization.
16 122 0.199966091100 Henry Cohn, 2025, needs more optimization.
16 124 0.199989165771 Henry Cohn, 2025, needs more optimization.
16 126 0.199994691163 Henry Cohn, 2025, needs more optimization.
16 127 0.199995845425 Henry Cohn, 2025, needs more optimization.
16 130 0.199999918321 Henry Cohn, 2025, needs more optimization.
16 159 0.202913709779 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
44⁢x2−4⁢x−1
16 160 0.204975438596 Henry Cohn, 2026, needs more optimization.
16 161 0.221710856870 Henry Cohn, 2026, needs more optimization.
16 162 0.229584483883 Henry Cohn, 2026, needs more optimization.
16 163 0.233527617435 Henry Cohn, 2026, needs more optimization.
16 164 0.236157326771 Henry Cohn, 2026, needs more optimization.
16 165 0.238144183808 Henry Cohn, 2026, needs more optimization.
16 166 0.239582841588 Henry Cohn, 2026, needs more optimization.
16 167 0.240932114456 Henry Cohn, 2026, needs more optimization.
16 168 0.242178407299 Henry Cohn, 2026, needs more optimization.
16 169 0.243006711157 Henry Cohn, 2026, needs more optimization.
16 170 0.244083626556 Henry Cohn, 2026, needs more optimization.
16 171 0.245114604983 Henry Cohn, 2026, needs more optimization.
16 172 0.245712824923 Henry Cohn, 2026, needs more optimization.
16 173 0.246008048456 Henry Cohn, 2026, needs more optimization.
16 174 0.246394977527 Henry Cohn, 2026, needs more optimization.
16 175 0.246783142655 Henry Cohn, 2026, needs more optimization.
16 176 0.247725000323 Henry Cohn, 2026, needs more optimization.
16 178 0.248074728173 Henry Cohn, 2026, needs more optimization.
16 179 0.248211352858 Henry Cohn, 2026, needs more optimization.
16 180 0.248538777471 Henry Cohn, 2026, needs more optimization.
16 181 0.248728855822 Henry Cohn, 2026, needs more optimization.
16 182 0.249198180783 Henry Cohn, 2026, needs more optimization.
16 183 0.249276453379 Henry Cohn, 2026, needs more optimization.
16 184 0.249337884492 Henry Cohn, 2026, needs more optimization.
16 185 0.249531552007 Henry Cohn, 2026, needs more optimization.
16 186 0.249698724842 Henry Cohn, 2026, needs more optimization.
16 187 0.249784002919 Henry Cohn, 2026, needs more optimization.
16 188 0.249850990152 Henry Cohn, 2026, needs more optimization.
16 189 0.249902134371 Henry Cohn, 2026, needs more optimization.
16 190 0.249913255634 Henry Cohn, 2026, needs more optimization.
16 191 0.249926192853 Henry Cohn, 2026, needs more optimization.
16 192 0.249933787850 Henry Cohn, 2026, needs more optimization.
16 193 0.249935645652 Henry Cohn, 2026, needs more optimization.
16 195 0.249953080310 Henry Cohn, 2026, needs more optimization.
16 196 0.249983903378 Henry Cohn, 2026, needs more optimization.
16 198 0.249999986639 Henry Cohn, 2026, needs more optimization.
16 288* 0.25 V. I. Levenšteĭn, Bounds for the maximal cardinality of a code with bounded modulus of the inner product (Russian), Dokl. Akad. Nauk SSSR 263 (1982), 1303–1308, English translation in Soviet Math. Dokl. 25 (1982), 526–531; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
4⁢x−1
16 289 0.290824645574 Henry Cohn, 2026, needs more optimization.
16 290 0.320698560822 Henry Cohn, 2026, needs more optimization.
16 291 0.320946615777 Henry Cohn, 2026, needs more optimization.
16 292 0.321609404202 Henry Cohn, 2026, needs more optimization.
16 293 0.321767393150 Henry Cohn, 2026, needs more optimization.
16 294 0.321970387495 Henry Cohn, 2026, needs more optimization.
16 295 0.322672396914 Henry Cohn, 2026, needs more optimization.
16 296 0.323121569619 Henry Cohn, 2026, needs more optimization.
16 297 0.323494114051 Henry Cohn, 2026, needs more optimization.
16 298 0.323789536022 Henry Cohn, 2026, needs more optimization.
16 299 0.324817825608 Henry Cohn, 2026, needs more optimization.
16 300 0.325173897496 Henry Cohn, 2026, needs more optimization.
16 304 0.325250802196 Henry Cohn, 2026, needs more optimization.
16 305 0.325530267005 Henry Cohn, 2026, needs more optimization.
16 308 0.326004103681 Henry Cohn, 2026, needs more optimization.
16 310 0.327908654128 Henry Cohn, 2026, needs more optimization.
16 311 0.327940969500 Henry Cohn, 2026, needs more optimization.
16 312 0.328117052249 Henry Cohn, 2026, needs more optimization.
16 315 0.328328223943 Henry Cohn, 2026, needs more optimization.
16 316 0.328385208881 Henry Cohn, 2026, needs more optimization.
16 317 0.328537943491 Henry Cohn, 2026, needs more optimization.
16 318 0.328664788428 Henry Cohn, 2026, needs more optimization.
16 320 0.328848737906 Henry Cohn, 2026, needs more optimization.
16 324 0.328966130649 Henry Cohn, 2026, needs more optimization.
16 325 0.329147111466 Henry Cohn, 2026, needs more optimization.
16 326 0.329358212193 Henry Cohn, 2026, needs more optimization.
16 512 0.333333333334 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
3⁢x−1
16 513 0.391899630247 Henry Cohn, 2025, needs more optimization.
16 514 0.391925212957 Henry Cohn, 2025, needs more optimization.
16 515 0.392184707636 Henry Cohn, 2025, needs more optimization.
16 516 0.392591412926 Henry Cohn, 2026, needs more optimization.
16 517 0.392634267266 Henry Cohn, 2025, needs more optimization.
16 518 0.392722638362 Henry Cohn, 2025, needs more optimization.
16 519 0.392822032060 Henry Cohn, 2025, needs more optimization.
16 520 0.392903207539 Henry Cohn, 2026, needs more optimization.
16 521 0.393133536522 Henry Cohn, 2025, needs more optimization.
16 522 0.393639694745 Henry Cohn, 2025, needs more optimization.
16 523 0.393642909640 Henry Cohn, 2025, needs more optimization.
16 524 0.394010879429 Henry Cohn, 2026, needs more optimization.
16 525 0.394048136884 Henry Cohn, 2025, needs more optimization.
16 526 0.394349206845 Henry Cohn, 2025, needs more optimization.
16 527 0.394364961294 Henry Cohn, 2025, needs more optimization.
16 528 0.394447496751 Henry Cohn, 2026, needs more optimization.
16 529 0.394734533399 Henry Cohn, 2025, needs more optimization.
16 530 0.394973218996 Henry Cohn, 2025, needs more optimization.
16 531 0.395372694593 Henry Cohn, 2025, needs more optimization.
16 532 0.395560759345 Henry Cohn, 2025, needs more optimization.
16 533 0.395856738708 Henry Cohn, 2025, needs more optimization.
16 534 0.395989958872 Henry Cohn, 2025, needs more optimization.
16 535 0.396176179232 Henry Cohn, 2025, needs more optimization.
16 536 0.396325004089 Henry Cohn, 2026, needs more optimization.
16 537 0.396383621089 Henry Cohn, 2025, needs more optimization.
16 538 0.396684273329 Henry Cohn, 2025, needs more optimization.
16 539 0.396705747724 Henry Cohn, 2025, needs more optimization.
16 540 0.397312657536 Henry Cohn, 2026, needs more optimization.
16 541 0.397369983799 Henry Cohn, 2025, needs more optimization.
16 542 0.397417287827 Henry Cohn, 2025, needs more optimization.
16 543 0.397713318899 Henry Cohn, 2025, needs more optimization.
16 544 0.397775330468 Henry Cohn, 2026, needs more optimization.
16 545 0.398404617655 Henry Cohn, 2025, needs more optimization.
16 546 0.398405841058 Henry Cohn, 2025, needs more optimization.
16 547 0.398553798594 Henry Cohn, 2025, needs more optimization.
16 548 0.398573298565 Henry Cohn, 2026, needs more optimization.
16 768 0.4 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
16 769 0.4 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
16 1024 0.428571428572 Subcode of a code of size 1056 from T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
7⁢x−3
17 35 0.044915529038 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3825⁢x3−289⁢x2−17⁢x+1
17 36 0.052701899358 Henry Cohn, 2025.
17 37 0.055949336674 Henry Cohn, 2026.
17 38 0.055983875620 Henry Cohn, 2025.
17 39 0.062879614874 Henry Cohn, 2024.
17 40 0.064964413617 Henry Cohn, 2025.
17 41 0.070153821556 Henry Cohn, 2025.
17 42 0.073269797523 Henry Cohn, 2025.
17 45 0.073591871415 Henry Cohn, 2023.
239⁢x2−4⁢x−1
17 46 0.080184930575 Henry Cohn, 2026.
17 52 0.084342587557 Henry Cohn, 2023.
188⁢x2−4⁢x−1
17 53 0.098937215086 Henry Cohn, 2024.
2304⁢x4−96⁢x3−95⁢x2−2⁢x+1
17 55 0.100854947492 Henry Cohn, 2026.
17 56 0.102993455487 Henry Cohn, 2026.
17 64 0.111111111112 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−1
17 65 0.121403722185 Henry Cohn, 2026, needs more optimization.
17 66 0.124823812635 Henry Cohn, 2026, needs more optimization.
17 67 0.127103338533 Henry Cohn, 2026, needs more optimization.
17 68 0.127214004902 Henry Cohn, 2026, needs more optimization.
17 69 0.127247527905 Henry Cohn, 2026, needs more optimization.
17 71 0.127270310008 Henry Cohn, 2025.
17 74 0.127284404862 Henry Cohn, 2025.
17 76 0.127284594471 Henry Cohn, 2025.
17 77 0.127303652500 Henry Cohn, 2025, needs more optimization.
17 78 0.135257083416 Henry Cohn, 2026, needs more optimization.
17 79 0.142565741403 Henry Cohn, 2026, needs more optimization.
17 80 0.148027287454 Henry Cohn, 2026, needs more optimization.
17 81 0.152542230093 Henry Cohn, 2026, needs more optimization.
17 82 0.156555839847 Henry Cohn, 2026, needs more optimization.
17 83 0.160375445397 Henry Cohn, 2026, needs more optimization.
17 84 0.163972509407 Henry Cohn, 2026, needs more optimization.
17 85 0.164063426175 Henry Cohn, 2026, needs more optimization.
17 86 0.165316098680 Henry Cohn, 2026, needs more optimization.
17 87 0.165352418023 Henry Cohn, 2026, needs more optimization.
17 88 0.166746746533 Henry Cohn, 2026, needs more optimization.
17 89 0.166838473395 Henry Cohn, 2026, needs more optimization.
17 90 0.167172864860 Henry Cohn, 2026, needs more optimization.
17 91 0.167321328702 Henry Cohn, 2026, needs more optimization.
17 92 0.167425672414 Henry Cohn, 2025, needs more optimization.
17 93 0.167574284587 Henry Cohn, 2026, needs more optimization.
17 94 0.167903583492 Henry Cohn, 2025, needs more optimization.
17 95 0.168041892502 Henry Cohn, 2026, needs more optimization.
17 96 0.168431850103 Henry Cohn, 2026, needs more optimization.
17 97 0.168538303449 Henry Cohn, 2026, needs more optimization.
17 98 0.168637510209 Henry Cohn, 2026, needs more optimization.
17 99 0.168674435901 Henry Cohn, 2026, needs more optimization.
17 100 0.168686853696 Henry Cohn, 2026, needs more optimization.
17 101 0.168708808391 Henry Cohn, 2026, needs more optimization.
17 104 0.170753175474 Orthogonal union of 102 points in 16 dimensions and 2 points in 1 dimension.
128⁢x2−16⁢x−1
17 105 0.170753914149 Henry Cohn, 2026, needs more optimization.
17 106 0.170757033121 Henry Cohn, 2026, needs more optimization.
17 107 0.170770206969 Henry Cohn, 2026, needs more optimization.
17 108 0.176361170883 Henry Cohn, 2026, needs more optimization.
17 109 0.179937491931 Henry Cohn, 2026, needs more optimization.
17 110 0.182018690389 Henry Cohn, 2026, needs more optimization.
17 111 0.183121687779 Henry Cohn, 2026, needs more optimization.
17 112 0.184651096470 Henry Cohn, 2026, needs more optimization.
17 113 0.185921325349 Henry Cohn, 2026, needs more optimization.
17 114 0.188137102044 Henry Cohn, 2026, needs more optimization.
17 116 0.189009800326 Henry Cohn, 2026, needs more optimization.
17 117 0.189789203020 Henry Cohn, 2026, needs more optimization.
17 118 0.190935511409 Henry Cohn, 2026, needs more optimization.
17 119 0.191925830194 Henry Cohn, 2026, needs more optimization.
17 120 0.193947471168 Henry Cohn, 2026, needs more optimization.
17 121 0.195096735316 Henry Cohn, 2026, needs more optimization.
17 122 0.196705622342 Henry Cohn, 2026, needs more optimization.
17 123 0.196832058862 Henry Cohn, 2026, needs more optimization.
17 124 0.196936839321 Henry Cohn, 2026, needs more optimization.
17 125 0.197288976274 Henry Cohn, 2026, needs more optimization.
17 126 0.197443296154 Henry Cohn, 2026, needs more optimization.
17 127 0.197638499999 Henry Cohn, 2025, needs more optimization.
17 128 0.197728301827 Henry Cohn, 2026, needs more optimization.
17 129 0.198745176169 Henry Cohn, 2026, needs more optimization.
17 130 0.199288775085 Henry Cohn, 2026, needs more optimization.
17 131 0.199317350125 Henry Cohn, 2026, needs more optimization.
17 132 0.199461219516 Henry Cohn, 2026, needs more optimization.
17 133 0.199776658734 Henry Cohn, 2026, needs more optimization.
17 134 0.199868467610 Henry Cohn, 2026, needs more optimization.
17 135 0.199978702167 Henry Cohn, 2026, needs more optimization.
17 136 0.200008020169 Henry Cohn, 2026, needs more optimization.
17 137 0.200164723446 Henry Cohn, 2026, needs more optimization.
17 138 0.202647219691 Henry Cohn, 2026, needs more optimization.
17 139 0.202672812477 Henry Cohn, 2026, needs more optimization.
17 140 0.202779710231 Henry Cohn, 2026, needs more optimization.
17 141 0.202833496678 Henry Cohn, 2026, needs more optimization.
17 142 0.202869693678 Henry Cohn, 2026, needs more optimization.
17 143 0.202875947997 Henry Cohn, 2026, needs more optimization.
17 144 0.202892430992 Henry Cohn, 2026, needs more optimization.
17 145 0.202894675427 Henry Cohn, 2026, needs more optimization.
17 146 0.202908434583 Henry Cohn, 2026, needs more optimization.
17 161 0.202913709779 Code with 159 points in 16 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
44⁢x2−4⁢x−1
17 162 0.202913709779 Henry Cohn, 2026.
44⁢x2−4⁢x−1
17 163 0.202921367864 Henry Cohn, 2026, needs more optimization.
17 164 0.202921657844 Henry Cohn, 2026, needs more optimization.
17 165 0.203276668748 Henry Cohn, 2026, needs more optimization.
17 168 0.209702872201 Henry Cohn, 2026, needs more optimization.
17 177 0.214580576913 Henry Cohn, 2026.
59⁢x2−8⁢x−1
17 178 0.217257934501 Henry Cohn, 2026, needs more optimization.
17 179 0.223983213975 Henry Cohn, 2026, needs more optimization.
17 180 0.224823311045 Henry Cohn, 2026, needs more optimization.
17 181 0.228430505051 Henry Cohn, 2026, needs more optimization.
17 182 0.230370962086 Henry Cohn, 2026, needs more optimization.
17 183 0.234365803266 Henry Cohn, 2026, needs more optimization.
17 184 0.237569555958 Henry Cohn, 2026, needs more optimization.
17 185 0.238814591550 Henry Cohn, 2026, needs more optimization.
17 186 0.239616337843 Henry Cohn, 2026, needs more optimization.
17 187 0.240522185788 Henry Cohn, 2026, needs more optimization.
17 188 0.241364555806 Henry Cohn, 2026, needs more optimization.
17 189 0.241554916107 Henry Cohn, 2026, needs more optimization.
17 190 0.242537305609 Henry Cohn, 2026, needs more optimization.
17 192 0.242776475199 Henry Cohn, 2026, needs more optimization.
17 196 0.242787820989 Henry Cohn, 2026, needs more optimization.
17 197 0.242788145735 Henry Cohn, 2026, needs more optimization.
17 198 0.242888766835 Henry Cohn, 2026, needs more optimization.
17 199 0.243157038197 Henry Cohn, 2026, needs more optimization.
17 200 0.243267109578 Henry Cohn, 2026, needs more optimization.
17 201 0.243780629208 Henry Cohn, 2026, needs more optimization.
17 202 0.244098929507 Henry Cohn, 2026, needs more optimization.
17 203 0.244220658249 Henry Cohn, 2026, needs more optimization.
17 204 0.244313832143 Henry Cohn, 2026, needs more optimization.
17 205 0.244593199206 Henry Cohn, 2026, needs more optimization.
17 206 0.244734953178 Henry Cohn, 2026, needs more optimization.
17 207 0.245128172466 Henry Cohn, 2026, needs more optimization.
17 208 0.245540394791 Henry Cohn, 2026, needs more optimization.
17 209 0.245683168255 Henry Cohn, 2026, needs more optimization.
17 210 0.245868779347 Henry Cohn, 2026, needs more optimization.
17 211 0.246211388648 Henry Cohn, 2026, needs more optimization.
17 212 0.246506363855 Henry Cohn, 2026, needs more optimization.
17 213 0.246761261821 Henry Cohn, 2026, needs more optimization.
17 214 0.246988013997 Henry Cohn, 2026, needs more optimization.
17 215 0.247321002676 Henry Cohn, 2026, needs more optimization.
17 216 0.247442974278 Henry Cohn, 2026, needs more optimization.
17 217 0.247599494655 Henry Cohn, 2026, needs more optimization.
17 218 0.247907498580 Henry Cohn, 2026, needs more optimization.
17 219 0.248199754103 Henry Cohn, 2026, needs more optimization.
17 220 0.248413062616 Henry Cohn, 2026, needs more optimization.
17 221 0.249985050505 Henry Cohn, 2026, needs more optimization.
17 292 0.25 Henry Cohn, 2026.
4⁢x−1
17 293 0.250107644001 Henry Cohn, 2026, needs more optimization.
17 316 0.261203876715 Henry Cohn, 2026, needs more optimization.
17 320 0.261203876882 Henry Cohn, 2026, needs more optimization.
17 321 0.284194766727 Henry Cohn, 2026, needs more optimization.
17 324 0.295918708986 Henry Cohn, 2026, needs more optimization.
17 326 0.300379517850 Henry Cohn, 2026, needs more optimization.
17 328 0.304222259662 Henry Cohn, 2026, needs more optimization.
17 332 0.304553600103 Henry Cohn, 2026, needs more optimization.
17 336 0.304638480718 Henry Cohn, 2026, needs more optimization.
17 337 0.304706956370 Henry Cohn, 2026, needs more optimization.
17 338 0.304706956576 Henry Cohn, 2026, needs more optimization.
17 339 0.304749836304 Henry Cohn, 2026, needs more optimization.
17 340 0.312890155346 Henry Cohn, 2026, needs more optimization.
17 342 0.313400491819 Henry Cohn, 2025, needs more optimization.
17 343 0.314841630605 Henry Cohn, 2025, needs more optimization.
17 344 0.314899169141 Henry Cohn, 2026, needs more optimization.
17 345 0.316057223042 Henry Cohn, 2025, needs more optimization.
17 346 0.316118437255 Henry Cohn, 2025, needs more optimization.
17 347 0.317382420133 Henry Cohn, 2025, needs more optimization.
17 348 0.317410084006 Henry Cohn, 2026, needs more optimization.
17 349 0.318631480893 Henry Cohn, 2025, needs more optimization.
17 350 0.318692686611 Henry Cohn, 2025, needs more optimization.
17 351 0.318842570612 Henry Cohn, 2025, needs more optimization.
17 352 0.320276065763 Henry Cohn, 2026, needs more optimization.
17 353 0.320358004020 Henry Cohn, 2025, needs more optimization.
17 354 0.322921276049 Henry Cohn, 2025, needs more optimization.
17 355 0.323240622037 Henry Cohn, 2025, needs more optimization.
17 356 0.324599002081 Henry Cohn, 2026, needs more optimization.
17 357 0.324674347760 Henry Cohn, 2025, needs more optimization.
17 358 0.324677522206 Henry Cohn, 2025, needs more optimization.
17 359 0.325570396391 Henry Cohn, 2025, needs more optimization.
17 360 0.325675052905 Henry Cohn, 2026, needs more optimization.
17 361 0.326299331409 Henry Cohn, 2025, needs more optimization.
17 362 0.326419782843 Henry Cohn, 2025, needs more optimization.
17 364 0.327607843411 Henry Cohn, 2026, needs more optimization.
17 365 0.327661166414 Henry Cohn, 2025, needs more optimization.
17 366 0.328605574205 Henry Cohn, 2025, needs more optimization.
17 367 0.329725269071 Henry Cohn, 2025, needs more optimization.
17 368 0.330432271058 Henry Cohn, 2026, needs more optimization.
17 546 0.333333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−1
17 578 0.333333333334 C. Ma, T. T. Zhaowei, P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
3⁢x−1
17 579 0.384386751984 Henry Cohn, 2025, needs more optimization.
17 580 0.384489580965 Henry Cohn, 2026, needs more optimization.
17 581 0.384499164779 Henry Cohn, 2025, needs more optimization.
17 582 0.384685553512 Henry Cohn, 2025, needs more optimization.
17 583 0.384901400690 Henry Cohn, 2025, needs more optimization.
17 584 0.384949959725 Henry Cohn, 2026, needs more optimization.
17 585 0.384966903624 Henry Cohn, 2025, needs more optimization.
17 586 0.385539098190 Henry Cohn, 2025, needs more optimization.
17 587 0.385541637903 Henry Cohn, 2025, needs more optimization.
17 588 0.385564523673 Henry Cohn, 2026, needs more optimization.
17 589 0.385951190150 Henry Cohn, 2025, needs more optimization.
17 590 0.386012719959 Henry Cohn, 2025, needs more optimization.
17 591 0.386020831990 Henry Cohn, 2025, needs more optimization.
17 592 0.386570929069 Henry Cohn, 2026, needs more optimization.
17 593 0.386655880734 Henry Cohn, 2025, needs more optimization.
17 594 0.386664779495 Henry Cohn, 2025, needs more optimization.
17 595 0.386764215489 Henry Cohn, 2025, needs more optimization.
17 596 0.387207370810 Henry Cohn, 2026, needs more optimization.
17 597 0.387277927498 Henry Cohn, 2025, needs more optimization.
17 598 0.387348389025 Henry Cohn, 2025, needs more optimization.
17 599 0.387399697539 Henry Cohn, 2025, needs more optimization.
17 600 0.387673206849 Henry Cohn, 2026, needs more optimization.
17 601 0.387717207601 Henry Cohn, 2025, needs more optimization.
17 602 0.387903020169 Henry Cohn, 2025, needs more optimization.
17 603 0.388274213435 Henry Cohn, 2025, needs more optimization.
17 604 0.388275605376 Henry Cohn, 2026, needs more optimization.
17 605 0.388352213522 Henry Cohn, 2025, needs more optimization.
17 606 0.388634596757 Henry Cohn, 2025, needs more optimization.
17 607 0.388865235140 Henry Cohn, 2025, needs more optimization.
17 608 0.388896952533 Henry Cohn, 2026, needs more optimization.
17 609 0.389131916372 Henry Cohn, 2025, needs more optimization.
17 610 0.389148122644 Henry Cohn, 2025, needs more optimization.
17 611 0.389517822003 Henry Cohn, 2025, needs more optimization.
17 612 0.389542958746 Henry Cohn, 2026, needs more optimization.
17 613 0.389589334878 Henry Cohn, 2025, needs more optimization.
17 614 0.389853435854 Henry Cohn, 2025, needs more optimization.
17 615 0.389911542351 Henry Cohn, 2025, needs more optimization.
17 616 0.390341304547 Henry Cohn, 2026, needs more optimization.
17 617 0.390365724717 Henry Cohn, 2025, needs more optimization.
17 619 0.390490728552 Henry Cohn, 2025, needs more optimization.
17 620 0.390690214187 Henry Cohn, 2026, needs more optimization.
17 621 0.390847575705 Henry Cohn, 2025, needs more optimization.
17 622 0.390850359831 Henry Cohn, 2025, needs more optimization.
17 624 0.391228368680 Henry Cohn, 2026, needs more optimization.
17 625 0.391368332007 Henry Cohn, 2025, needs more optimization.
17 626 0.391433589471 Henry Cohn, 2025, needs more optimization.
17 628 0.391878103269 Henry Cohn, 2025, needs more optimization.
17 629 0.391929328039 Henry Cohn, 2025, needs more optimization.
17 630 0.392005373070 Henry Cohn, 2025, needs more optimization.
17 631 0.392605304895 Henry Cohn, 2025, needs more optimization.
17 632 0.392625871423 Henry Cohn, 2026, needs more optimization.
17 633 0.392644325274 Henry Cohn, 2025, needs more optimization.
17 634 0.392992152076 Henry Cohn, 2025, needs more optimization.
17 635 0.393018103881 Henry Cohn, 2025, needs more optimization.
17 636 0.393036322130 Henry Cohn, 2026, needs more optimization.
17 637 0.393225216195 Henry Cohn, 2025, needs more optimization.
17 638 0.393595469493 Henry Cohn, 2025, needs more optimization.
17 639 0.393615961966 Henry Cohn, 2025, needs more optimization.
17 640 0.393850893355 Henry Cohn, 2026, needs more optimization.
17 641 0.393861933375 Henry Cohn, 2025, needs more optimization.
17 642 0.394141354266 Henry Cohn, 2025, needs more optimization.
17 643 0.394162888867 Henry Cohn, 2025, needs more optimization.
17 644 0.394217615501 Henry Cohn, 2026, needs more optimization.
17 645 0.394374143224 Henry Cohn, 2025, needs more optimization.
17 646 0.394733161798 Henry Cohn, 2025, needs more optimization.
17 647 0.394865721173 Henry Cohn, 2025, needs more optimization.
17 648 0.394885748828 Henry Cohn, 2026, needs more optimization.
17 649 0.395122837140 Henry Cohn, 2025, needs more optimization.
17 650 0.395183309253 Henry Cohn, 2025, needs more optimization.
17 651 0.395207336902 Henry Cohn, 2025, needs more optimization.
17 652 0.395686916140 Henry Cohn, 2026, needs more optimization.
17 653 0.395761077950 Henry Cohn, 2025, needs more optimization.
17 654 0.395813065070 Henry Cohn, 2025, needs more optimization.
17 655 0.395835524001 Henry Cohn, 2025, needs more optimization.
17 656 0.396208971634 Henry Cohn, 2026, needs more optimization.
17 657 0.396236676884 Henry Cohn, 2025, needs more optimization.
17 658 0.396244518720 Henry Cohn, 2025, needs more optimization.
17 659 0.396393049348 Henry Cohn, 2025, needs more optimization.
17 660 0.396650867275 Henry Cohn, 2026, needs more optimization.
17 661 0.396741644621 Henry Cohn, 2025, needs more optimization.
17 662 0.396996114325 Henry Cohn, 2025, needs more optimization.
17 663 0.397022110102 Henry Cohn, 2025, needs more optimization.
17 664 0.397062837170 Henry Cohn, 2026, needs more optimization.
17 665 0.397074844999 Henry Cohn, 2025, needs more optimization.
17 666 0.397621121011 Henry Cohn, 2025, needs more optimization.
17 667 0.397922919863 Henry Cohn, 2025, needs more optimization.
17 668 0.397951526077 Henry Cohn, 2026, needs more optimization.
17 669 0.398232768001 Henry Cohn, 2025, needs more optimization.
17 670 0.398269006061 Henry Cohn, 2025, needs more optimization.
17 672 0.398532721303 Henry Cohn, 2026, needs more optimization.
17 673 0.398547114794 Henry Cohn, 2025, needs more optimization.
17 674 0.398836644526 Henry Cohn, 2025, needs more optimization.
17 771 0.4 Orthogonal union of 769 points in 16 dimensions and 2 points in 1 dimension.
5⁢x−2
17 772 0.400015816743 Henry Cohn, 2026, needs more optimization.
17 773 0.400022561896 Henry Cohn, 2025, needs more optimization.
17 774 0.411072445623 Henry Cohn, 2026, needs more optimization.
17 775 0.411084956436 Henry Cohn, 2025, needs more optimization.
17 776 0.411377744053 Henry Cohn, 2026, needs more optimization.
17 777 0.411428319972 Henry Cohn, 2025, needs more optimization.
17 778 0.411456142080 Henry Cohn, 2026, needs more optimization.
17 779 0.411774744978 Henry Cohn, 2025, needs more optimization.
17 780 0.411785311602 Henry Cohn, 2026, needs more optimization.
17 781 0.411850362952 Henry Cohn, 2025, needs more optimization.
17 782 0.412060685354 Henry Cohn, 2026, needs more optimization.
17 783 0.412075730897 Henry Cohn, 2025, needs more optimization.
17 784 0.412301978580 Henry Cohn, 2026, needs more optimization.
17 785 0.412313644287 Henry Cohn, 2025, needs more optimization.
17 786 0.412394157061 Henry Cohn, 2026, needs more optimization.
17 787 0.412785425115 Henry Cohn, 2025, needs more optimization.
17 788 0.412790458138 Henry Cohn, 2026, needs more optimization.
17 789 0.412832246084 Henry Cohn, 2025, needs more optimization.
17 790 0.413138707314 Henry Cohn, 2026, needs more optimization.
17 791 0.413161576394 Henry Cohn, 2025, needs more optimization.
17 792 0.413166606292 Henry Cohn, 2026, needs more optimization.
17 793 0.413204447952 Henry Cohn, 2025, needs more optimization.
17 794 0.413526424265 Henry Cohn, 2026, needs more optimization.
17 795 0.413574430036 Henry Cohn, 2025, needs more optimization.
17 796 0.413607535542 Henry Cohn, 2026, needs more optimization.
17 797 0.413669222131 Henry Cohn, 2025, needs more optimization.
17 798 0.413780848941 Henry Cohn, 2026, needs more optimization.
17 799 0.414137970934 Henry Cohn, 2025, needs more optimization.
17 800 0.414143155809 Henry Cohn, 2026, needs more optimization.
17 801 0.414152368895 Henry Cohn, 2025, needs more optimization.
17 802 0.414198331515 Henry Cohn, 2026, needs more optimization.
17 803 0.414464466595 Henry Cohn, 2025, needs more optimization.
17 804 0.414473289276 Henry Cohn, 2026, needs more optimization.
17 805 0.414492954242 Henry Cohn, 2025, needs more optimization.
17 806 0.414838427665 Henry Cohn, 2026, needs more optimization.
17 807 0.414851426398 Henry Cohn, 2025, needs more optimization.
17 808 0.414867129605 Henry Cohn, 2026, needs more optimization.
17 809 0.414992441054 Henry Cohn, 2025, needs more optimization.
17 810 0.415034375897 Henry Cohn, 2026, needs more optimization.
17 811 0.415046825429 Henry Cohn, 2025, needs more optimization.
17 812 0.415442015846 Henry Cohn, 2026, needs more optimization.
17 813 0.415465093504 Henry Cohn, 2025, needs more optimization.
17 814 0.415493032647 Henry Cohn, 2026, needs more optimization.
17 815 0.415875048118 Henry Cohn, 2025, needs more optimization.
17 816 0.415887573019 Henry Cohn, 2026, needs more optimization.
17 817 0.415907955023 Henry Cohn, 2025, needs more optimization.
17 818 0.416094474108 Henry Cohn, 2026, needs more optimization.
17 819 0.416130794227 Henry Cohn, 2025, needs more optimization.
17 820 0.416336035615 Henry Cohn, 2026, needs more optimization.
17 821 0.416353133665 Henry Cohn, 2025, needs more optimization.
17 822 0.416635361342 Henry Cohn, 2026, needs more optimization.
17 824 0.416650604132 Henry Cohn, 2026, needs more optimization.
17 825 0.416671727325 Henry Cohn, 2025, needs more optimization.
17 826 0.416675441463 Henry Cohn, 2026, needs more optimization.
17 828 0.416907328036 Henry Cohn, 2026, needs more optimization.
17 829 0.417300605071 Henry Cohn, 2025, needs more optimization.
17 830 0.417338360099 Henry Cohn, 2026, needs more optimization.
17 831 0.417405991469 Henry Cohn, 2025, needs more optimization.
17 832 0.417550908223 Henry Cohn, 2026, needs more optimization.
17 833 0.417560049988 Henry Cohn, 2025, needs more optimization.
17 834 0.417564498196 Henry Cohn, 2026, needs more optimization.
17 835 0.417620249090 Henry Cohn, 2025, needs more optimization.
17 836 0.418054361132 Henry Cohn, 2026, needs more optimization.
17 837 0.418079431589 Henry Cohn, 2025, needs more optimization.
17 838 0.418088762005 Henry Cohn, 2026, needs more optimization.
17 839 0.418322507555 Henry Cohn, 2025, needs more optimization.
17 840 0.418326928163 Henry Cohn, 2026, needs more optimization.
17 841 0.418389792343 Henry Cohn, 2025, needs more optimization.
17 842 0.418637388893 Henry Cohn, 2026, needs more optimization.
17 843 0.418647876178 Henry Cohn, 2025, needs more optimization.
17 844 0.418653519023 Henry Cohn, 2026, needs more optimization.
17 845 0.418957287057 Henry Cohn, 2025, needs more optimization.
17 846 0.418961244591 Henry Cohn, 2026, needs more optimization.
17 847 0.419307760198 Henry Cohn, 2025, needs more optimization.
17 848 0.419467135138 Henry Cohn, 2026, needs more optimization.
17 849 0.419485178712 Henry Cohn, 2025, needs more optimization.
17 850 0.419488840831 Henry Cohn, 2026, needs more optimization.
17 851 0.419534995750 Henry Cohn, 2025, needs more optimization.
17 852 0.419783382270 Henry Cohn, 2026, needs more optimization.
17 853 0.419794119142 Henry Cohn, 2025, needs more optimization.
17 854 0.420101143691 Henry Cohn, 2026, needs more optimization.
17 855 0.420173932125 Henry Cohn, 2025, needs more optimization.
17 856 0.420198134879 Henry Cohn, 2026, needs more optimization.
17 857 0.420215461401 Henry Cohn, 2025, needs more optimization.
17 858 0.420221329202 Henry Cohn, 2026, needs more optimization.
17 859 0.420414663543 Henry Cohn, 2025, needs more optimization.
17 860 0.420435622319 Henry Cohn, 2026, needs more optimization.
17 861 0.420694111061 Henry Cohn, 2025, needs more optimization.
17 862 0.420720566373 Henry Cohn, 2026, needs more optimization.
17 863 0.420797260097 Henry Cohn, 2025, needs more optimization.
17 864 0.420800233866 Henry Cohn, 2026, needs more optimization.
17 865 0.420826129155 Henry Cohn, 2025, needs more optimization.
17 866 0.420893057165 Henry Cohn, 2026, needs more optimization.
17 867 0.421194066406 Henry Cohn, 2025, needs more optimization.
17 868 0.421196600618 Henry Cohn, 2026, needs more optimization.
17 869 0.421226830560 Henry Cohn, 2025, needs more optimization.
17 870 0.421304794457 Henry Cohn, 2026, needs more optimization.
17 871 0.421706574960 Henry Cohn, 2025, needs more optimization.
17 872 0.421730751141 Henry Cohn, 2026, needs more optimization.
17 873 0.421877057938 Henry Cohn, 2025, needs more optimization.
17 874 0.421908097048 Henry Cohn, 2026, needs more optimization.
17 875 0.422078665519 Henry Cohn, 2025, needs more optimization.
17 876 0.422266429629 Henry Cohn, 2026, needs more optimization.
17 877 0.422277481212 Henry Cohn, 2025, needs more optimization.
17 878 0.422279298293 Henry Cohn, 2026, needs more optimization.
17 879 0.422661431809 Henry Cohn, 2025, needs more optimization.
17 880 0.422670773039 Henry Cohn, 2026, needs more optimization.
17 881 0.422672563066 Henry Cohn, 2025, needs more optimization.
17 882 0.422675526014 Henry Cohn, 2026, needs more optimization.
17 883 0.422712133944 Henry Cohn, 2025, needs more optimization.
17 884 0.422816554663 Henry Cohn, 2026, needs more optimization.
17 885 0.422882244676 Henry Cohn, 2025, needs more optimization.
17 886 0.423205687570 Henry Cohn, 2026, needs more optimization.
17 887 0.423218411168 Henry Cohn, 2025, needs more optimization.
17 888 0.423271999218 Henry Cohn, 2026, needs more optimization.
17 889 0.423303631557 Henry Cohn, 2025, needs more optimization.
17 890 0.423307880857 Henry Cohn, 2026, needs more optimization.
17 891 0.423466479008 Henry Cohn, 2025, needs more optimization.
17 892 0.423679842703 Henry Cohn, 2026, needs more optimization.
17 893 0.423715198583 Henry Cohn, 2025, needs more optimization.
17 894 0.423749261584 Henry Cohn, 2026, needs more optimization.
17 895 0.423980219720 Henry Cohn, 2025, needs more optimization.
17 896 0.423981096147 Henry Cohn, 2026, needs more optimization.
17 897 0.423997831890 Henry Cohn, 2025, needs more optimization.
17 898 0.424162508087 Henry Cohn, 2026, needs more optimization.
17 899 0.424177966744 Henry Cohn, 2025, needs more optimization.
17 900 0.424179997347 Henry Cohn, 2026, needs more optimization.
17 901 0.424483312926 Henry Cohn, 2025, needs more optimization.
17 902 0.424494416529 Henry Cohn, 2026, needs more optimization.
17 903 0.424624928984 Henry Cohn, 2025, needs more optimization.
17 904 0.424867718417 Henry Cohn, 2026, needs more optimization.
17 905 0.424884184079 Henry Cohn, 2025, needs more optimization.
17 906 0.424933793269 Henry Cohn, 2026, needs more optimization.
17 907 0.425084985086 Henry Cohn, 2025, needs more optimization.
17 908 0.425218804645 Henry Cohn, 2026, needs more optimization.
17 909 0.425236552243 Henry Cohn, 2025, needs more optimization.
17 910 0.425244760355 Henry Cohn, 2026, needs more optimization.
17 911 0.425562235092 Henry Cohn, 2025, needs more optimization.
17 912 0.425567139226 Henry Cohn, 2026, needs more optimization.
17 913 0.425618586570 Henry Cohn, 2025, needs more optimization.
17 914 0.425935399453 Henry Cohn, 2026, needs more optimization.
17 916 0.425974475974 Henry Cohn, 2026, needs more optimization.
17 917 0.426243670802 Henry Cohn, 2025, needs more optimization.
17 918 0.426256445493 Henry Cohn, 2026, needs more optimization.
17 919 0.426325470151 Henry Cohn, 2025, needs more optimization.
17 920 0.426533376500 Henry Cohn, 2026, needs more optimization.
17 921 0.426541193565 Henry Cohn, 2025, needs more optimization.
17 922 0.426717992115 Henry Cohn, 2026, needs more optimization.
17 924 0.426827699525 Henry Cohn, 2026, needs more optimization.
17 925 0.426874837261 Henry Cohn, 2025, needs more optimization.
17 926 0.427227099531 Henry Cohn, 2026, needs more optimization.
17 927 0.427278425952 Henry Cohn, 2025, needs more optimization.
17 928 0.427288884466 Henry Cohn, 2026, needs more optimization.
17 929 0.427302674882 Henry Cohn, 2025, needs more optimization.
17 1024 0.428571428572 Subcode of a code of size 1570 from T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
7⁢x−3
18 37 0.042671058118 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
4608⁢x3−324⁢x2−18⁢x+1
18 38 0.050097352046 Henry Cohn, 2025.
18 39 0.055224148787 Henry Cohn, 2025.
18 40 0.055678193348 Henry Cohn, 2025.
1856⁢x4+736⁢x3+204⁢x2+4⁢x−1
18 41 0.060967744952 Henry Cohn, 2023.
18 42 0.063513513654 Henry Cohn, 2023.
18 43 0.066629754705 Henry Cohn, 2025.
18 44 0.066804066179 Henry Cohn, 2023.
18 45 0.071480323505 Henry Cohn, 2026.
18 46 0.073552043366 Henry Cohn, 2025.
18 47 0.073575768177 Henry Cohn, 2025.
18 48 0.074706792917 Henry Cohn, 2024.
18 50 0.078219048073 Henry Cohn, 2025.
368⁢x2−16⁢x−1
18 51 0.084340252912 Henry Cohn, 2025.
18 52 0.084342002724 Henry Cohn, 2025.
18 53 0.084342450321 Henry Cohn, 2025.
18 54 0.084342552633 Henry Cohn, 2025.
18 55 0.087707155784 Henry Cohn, 2025.
18 57 0.092724727985 Henry Cohn, 2025.
332⁢x2−20⁢x−1
18 59 0.096317631192 Henry Cohn, 2025.
18 60 0.096621974569 Henry Cohn, 2025.
18 69 0.101456854890 Henry Cohn, 2024.
176⁢x2−8⁢x−1
18 71 0.107360417204 Henry Cohn, 2026, needs more optimization.
18 72 0.109540130291 Henry Cohn, 2026, needs more optimization.
18 73 0.117134464854 Henry Cohn, 2026, needs more optimization.
18 74 0.121825115439 Henry Cohn, 2026, needs more optimization.
18 76 0.122045963410 Henry Cohn, 2026, needs more optimization.
18 77 0.123493846412 Henry Cohn, 2026, needs more optimization.
18 78 0.125826683534 Henry Cohn, 2026, needs more optimization.
18 80 0.126224060075 Henry Cohn, 2026, needs more optimization.
18 81 0.126904281674 Henry Cohn, 2026, needs more optimization.
18 82 0.127626718472 Henry Cohn, 2026, needs more optimization.
18 83 0.129098845419 Henry Cohn, 2026, needs more optimization.
18 84 0.130581918400 Henry Cohn, 2026, needs more optimization.
18 85 0.132295645173 Henry Cohn, 2026, needs more optimization.
18 86 0.132700084117 Henry Cohn, 2026, needs more optimization.
18 87 0.133675592670 Henry Cohn, 2026, needs more optimization.
18 88 0.134264346430 Henry Cohn, 2025.
18 96 0.142857142858 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−1
18 97 0.152402949200 Henry Cohn, 2026.
16⁢x2−9⁢x+1
18 98 0.155249851797 Henry Cohn, 2026, needs more optimization.
18 99 0.165211710795 Henry Cohn, 2026, needs more optimization.
18 100 0.167512152817 Henry Cohn, 2026, needs more optimization.
18 101 0.167585331503 Henry Cohn, 2026, needs more optimization.
18 102 0.168091778641 Henry Cohn, 2026, needs more optimization.
18 103 0.168582537376 Henry Cohn, 2026, needs more optimization.
18 104 0.169042218512 Henry Cohn, 2026, needs more optimization.
18 105 0.169059474211 Henry Cohn, 2026, needs more optimization.
18 106 0.169231003773 Henry Cohn, 2026, needs more optimization.
18 107 0.169525752017 Henry Cohn, 2026, needs more optimization.
18 108 0.170156210108 Henry Cohn, 2026, needs more optimization.
18 109 0.170449701157 Henry Cohn, 2026, needs more optimization.
18 110 0.170631915683 Henry Cohn, 2026, needs more optimization.
18 111 0.170820617686 Henry Cohn, 2026, needs more optimization.
18 112 0.171627564390 Henry Cohn, 2026, needs more optimization.
18 113 0.172991187581 Henry Cohn, 2026, needs more optimization.
18 114 0.175540853941 Henry Cohn, 2026, needs more optimization.
18 115 0.177868596063 Henry Cohn, 2026, needs more optimization.
18 116 0.179458482342 Henry Cohn, 2026, needs more optimization.
18 117 0.181388785750 Henry Cohn, 2026, needs more optimization.
18 118 0.183022569146 Henry Cohn, 2026, needs more optimization.
18 119 0.185088015247 Henry Cohn, 2026, needs more optimization.
18 120 0.185217299571 Henry Cohn, 2026, needs more optimization.
18 121 0.186200976847 Henry Cohn, 2026, needs more optimization.
18 122 0.187424029518 Henry Cohn, 2026, needs more optimization.
18 130 0.189193290536 Henry Cohn, 2026, needs more optimization.
18 132 0.191489361703 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
47⁢x−9
18 133 0.193070622518 Henry Cohn, 2026, needs more optimization.
18 134 0.193721012479 Henry Cohn, 2026, needs more optimization.
18 135 0.194298495175 Henry Cohn, 2026, needs more optimization.
18 136 0.194623027040 Henry Cohn, 2026, needs more optimization.
18 137 0.194954693374 Henry Cohn, 2026, needs more optimization.
18 138 0.195230197730 Henry Cohn, 2026, needs more optimization.
18 140 0.195281232520 Henry Cohn, 2026, needs more optimization.
18 144 0.2 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
5⁢x−1
18 146 0.200557378588 Henry Cohn, 2026, needs more optimization.
18 150 0.200749455424 Henry Cohn, 2026, needs more optimization.
18 151 0.200894711605 Henry Cohn, 2026, needs more optimization.
18 152 0.200984408985 Henry Cohn, 2026, needs more optimization.
18 153 0.201189772934 Henry Cohn, 2026, needs more optimization.
18 154 0.201422256036 Henry Cohn, 2026, needs more optimization.
18 155 0.201456188190 Henry Cohn, 2026, needs more optimization.
18 156 0.201493543981 Henry Cohn, 2026, needs more optimization.
18 157 0.201639258867 Henry Cohn, 2026, needs more optimization.
18 159 0.201643956418 Henry Cohn, 2026, needs more optimization.
18 160 0.201667601119 Henry Cohn, 2026, needs more optimization.
18 161 0.202315871229 Henry Cohn, 2026, needs more optimization.
18 163 0.202373950270 Henry Cohn, 2026, needs more optimization.
18 164 0.202540673077 Henry Cohn, 2026, needs more optimization.
18 165 0.202761305477 Henry Cohn, 2026, needs more optimization.
18 166 0.202859143239 Henry Cohn, 2026, needs more optimization.
18 167 0.202898281394 Henry Cohn, 2026, needs more optimization.
18 170 0.202919972291 Henry Cohn, 2026, needs more optimization.
18 171 0.203189812067 Henry Cohn, 2026, needs more optimization.
18 172 0.204449666594 Henry Cohn, 2026, needs more optimization.
18 173 0.207751306918 Henry Cohn, 2026, needs more optimization.
18 174 0.210250360649 Henry Cohn, 2026, needs more optimization.
18 175 0.213355895456 Henry Cohn, 2026, needs more optimization.
18 179 0.214580576913 Orthogonal union of 177 points in 17 dimensions and 2 points in 1 dimension.
59⁢x2−8⁢x−1
18 181 0.214589440531 Henry Cohn, 2026, needs more optimization.
18 182 0.214605193575 Henry Cohn, 2026, needs more optimization.
18 185 0.214629675142 Henry Cohn, 2026, needs more optimization.
18 186 0.216565147457 Henry Cohn, 2026, needs more optimization.
18 187 0.217462630573 Henry Cohn, 2026, needs more optimization.
18 188 0.217858125145 Henry Cohn, 2026, needs more optimization.
18 189 0.219809682391 Henry Cohn, 2026, needs more optimization.
18 190 0.220542697259 Henry Cohn, 2026, needs more optimization.
18 191 0.222069373684 Henry Cohn, 2026, needs more optimization.
18 192 0.224035162747 Henry Cohn, 2026, needs more optimization.
18 205 0.224489795919 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
49⁢x−11
18 206 0.227401911664 Henry Cohn, 2026, needs more optimization.
18 207 0.228476634022 Henry Cohn, 2026, needs more optimization.
18 208 0.229747226174 Henry Cohn, 2026, needs more optimization.
18 209 0.230552070313 Henry Cohn, 2026, needs more optimization.
18 210 0.230996747459 Henry Cohn, 2026, needs more optimization.
18 211 0.231265700970 Henry Cohn, 2026, needs more optimization.
18 212 0.232483482007 Henry Cohn, 2026, needs more optimization.
18 213 0.233085742068 Henry Cohn, 2026, needs more optimization.
18 215 0.235426555646 Henry Cohn, 2026, needs more optimization.
18 216 0.235443106342 Henry Cohn, 2026, needs more optimization.
18 217 0.237693457894 Henry Cohn, 2026, needs more optimization.
18 218 0.237693457897 Henry Cohn, 2026, needs more optimization.
18 219 0.237870437110 Henry Cohn, 2026, needs more optimization.
18 220 0.241117521283 Henry Cohn, 2026, needs more optimization.
18 221 0.241242932871 Henry Cohn, 2026, needs more optimization.
18 222 0.241411122360 Henry Cohn, 2026, needs more optimization.
18 223 0.241509392725 Henry Cohn, 2026, needs more optimization.
18 224 0.242447660058 Henry Cohn, 2026, needs more optimization.
18 225 0.242796211427 Henry Cohn, 2026, needs more optimization.
18 226 0.243104238993 Henry Cohn, 2026, needs more optimization.
18 228 0.243305761169 Henry Cohn, 2026, needs more optimization.
18 229 0.243466866615 Henry Cohn, 2026, needs more optimization.
18 230 0.244122957874 Henry Cohn, 2026, needs more optimization.
18 231 0.244159247927 Henry Cohn, 2026, needs more optimization.
18 232 0.244197973463 Henry Cohn, 2026, needs more optimization.
18 256 0.246437044504 Henry Cohn, 2026, needs more optimization.
18 257 0.246787981720 Henry Cohn, 2025, needs more optimization.
18 260 0.247104074684 Henry Cohn, 2025, needs more optimization.
18 261 0.247126454539 Henry Cohn, 2026, needs more optimization.
18 262 0.247159741095 Henry Cohn, 2025, needs more optimization.
18 263 0.247191335203 Henry Cohn, 2025, needs more optimization.
18 264 0.247212300667 Henry Cohn, 2025, needs more optimization.
18 265 0.247289888703 Henry Cohn, 2025, needs more optimization.
18 266 0.247360813446 Henry Cohn, 2025, needs more optimization.
18 267 0.247394795521 Henry Cohn, 2025, needs more optimization.
18 268 0.247489610910 Henry Cohn, 2025, needs more optimization.
18 269 0.247492387801 Henry Cohn, 2025, needs more optimization.
18 270 0.247510978203 Henry Cohn, 2025, needs more optimization.
18 271 0.247554974434 Henry Cohn, 2026, needs more optimization.
18 272 0.247588413101 Henry Cohn, 2025, needs more optimization.
18 273 0.247601988251 Henry Cohn, 2025, needs more optimization.
18 274 0.247610943409 Henry Cohn, 2025, needs more optimization.
18 276 0.247661604596 Henry Cohn, 2025, needs more optimization.
18 277 0.247714163483 Henry Cohn, 2025, needs more optimization.
18 278 0.247740576377 Henry Cohn, 2025, needs more optimization.
18 280 0.247754588482 Henry Cohn, 2025, needs more optimization.
18 282 0.247830057904 Henry Cohn, 2026, needs more optimization.
18 286 0.247864612414 Henry Cohn, 2026, needs more optimization.
18 287 0.248707750538 Henry Cohn, 2026, needs more optimization.
18 288 0.248892043394 Henry Cohn, 2026, needs more optimization.
18 289 0.248943124800 Henry Cohn, 2025, needs more optimization.
18 290 0.249341399134 Henry Cohn, 2026, needs more optimization.
18 291 0.249410609573 Henry Cohn, 2026, needs more optimization.
18 292 0.249507024422 Henry Cohn, 2025, needs more optimization.
18 296 0.25 Henry Cohn, 2026.
4⁢x−1
18 300 0.250104964694 Henry Cohn, 2026, needs more optimization.
18 301 0.250104964716 Henry Cohn, 2025, needs more optimization.
18 302 0.250123060329 Henry Cohn, 2025, needs more optimization.
18 303 0.251311867492 Henry Cohn, 2026, needs more optimization.
18 304 0.259265953487 Henry Cohn, 2026, needs more optimization.
18 305 0.259369064427 Henry Cohn, 2025, needs more optimization.
18 307 0.259439567247 Henry Cohn, 2025, needs more optimization.
18 308 0.259927411708 Henry Cohn, 2026, needs more optimization.
18 312 0.260092303960 Henry Cohn, 2026, needs more optimization.
18 316 0.260117731035 Henry Cohn, 2026, needs more optimization.
18 318 0.260464842805 Henry Cohn, 2025, needs more optimization.
18 319 0.260531286407 Henry Cohn, 2025, needs more optimization.
18 320 0.261111039640 Henry Cohn, 2026, needs more optimization.
18 324 0.261122073875 Henry Cohn, 2026, needs more optimization.
18 326 0.295918708986 Orthogonal union of 324 points in 17 dimensions and 2 points in 1 dimension.
18 364 0.296296296297 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
27⁢x−8
18 480 0.296296296297 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
27⁢x−8
18 481 0.298586129437 Henry Cohn, 2025, needs more optimization.
18 482 0.300581695675 Henry Cohn, 2025, needs more optimization.
18 483 0.301586559090 Henry Cohn, 2025, needs more optimization.
18 672 0.333333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−1
18 867 0.357142857143 Henry Cohn, 2025, by modifying a construction from C. Ma, T. T. Zhaowei, P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
14⁢x−5
18 870 0.385446301777 Henry Cohn, 2026, needs more optimization.
18 874 0.385536132699 Henry Cohn, 2026, needs more optimization.
18 878 0.385642331921 Henry Cohn, 2026, needs more optimization.
18 882 0.385735867202 Henry Cohn, 2026, needs more optimization.
18 886 0.385831910085 Henry Cohn, 2026, needs more optimization.
18 890 0.385989543307 Henry Cohn, 2026, needs more optimization.
18 894 0.386358701849 Henry Cohn, 2026, needs more optimization.
18 898 0.386650937123 Henry Cohn, 2026, needs more optimization.
18 902 0.386847870865 Henry Cohn, 2026, needs more optimization.
18 906 0.387121700823 Henry Cohn, 2026, needs more optimization.
18 910 0.387288304036 Henry Cohn, 2026, needs more optimization.
18 914 0.387450251605 Henry Cohn, 2026, needs more optimization.
18 918 0.387617648860 Henry Cohn, 2026, needs more optimization.
18 922 0.387877860961 Henry Cohn, 2026, needs more optimization.
18 926 0.388079214659 Henry Cohn, 2026, needs more optimization.
18 930 0.388331451714 Henry Cohn, 2026, needs more optimization.
18 934 0.388703249071 Henry Cohn, 2026, needs more optimization.
18 938 0.388958585503 Henry Cohn, 2026, needs more optimization.
18 942 0.389223696398 Henry Cohn, 2026, needs more optimization.
18 946 0.389494706031 Henry Cohn, 2026, needs more optimization.
18 950 0.389902997433 Henry Cohn, 2026, needs more optimization.
18 954 0.390143627527 Henry Cohn, 2026, needs more optimization.
18 958 0.390435583374 Henry Cohn, 2026, needs more optimization.
18 962 0.390626905101 Henry Cohn, 2026, needs more optimization.
18 966 0.390831425594 Henry Cohn, 2026, needs more optimization.
18 970 0.391082531856 Henry Cohn, 2026, needs more optimization.
18 974 0.391348349722 Henry Cohn, 2026, needs more optimization.
18 978 0.391826905058 Henry Cohn, 2026, needs more optimization.
18 982 0.392313561078 Henry Cohn, 2026, needs more optimization.
18 986 0.392826999268 Henry Cohn, 2026, needs more optimization.
18 990 0.393371357801 Henry Cohn, 2026, needs more optimization.
18 994 0.394186238610 Henry Cohn, 2026, needs more optimization.
18 996 0.395047828358 Henry Cohn, 2026, needs more optimization.
18 997 0.395938146558 Henry Cohn, 2026, needs more optimization.
18 1024 0.4 Henry Cohn, 2025, subcode of a code of size 1156 obtained by modifying a construction from C. Ma, T. T. Zhaowei, P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
5⁢x−2
19 39 0.040648168399 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5491⁢x3−361⁢x2−19⁢x+1
19 40 0.047619047620 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
21⁢x−1
19 41 0.053165944699 Henry Cohn, 2023.
19 42 0.053978364917 Henry Cohn, 2025.
19 43 0.058551084358 Henry Cohn, 2025.
19 44 0.059131790994 Henry Cohn, 2023.
19 45 0.059418524383 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
19 48 0.063706690497 Henry Cohn, 2023.
215⁢x2+2⁢x−1
19 50 0.069767441861 Henry Cohn, 2023.
43⁢x−3
19 51 0.075275141543 Henry Cohn, 2025.
19 52 0.077608632538 Henry Cohn, 2026, needs more optimization.
19 53 0.080493593475 Henry Cohn, 2026.
19 54 0.081692292171 Henry Cohn, 2025.
19 55 0.082178889828 Henry Cohn, 2025.
19 56 0.083233613341 Henry Cohn, 2026, needs more optimization.
19 57 0.084818962260 Henry Cohn, 2025.
19 60 0.090909090910 Kissing configuration of 81 points in 20 dimensions from A. E. Brouwer and W. H. Haemers, Structure and uniqueness of the (81,20,1,6) strongly regular graph, Discrete Math. 106/107 (1992), 77–82, doi:10.1016/0012-365X(92)90532-K.
11⁢x−1
19 62 0.093346164763 Henry Cohn, 2026.
479⁢x2−34⁢x−1
19 66 0.097744360903 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
133⁢x−13
19 69 0.101319957448 Henry Cohn, 2026, needs more optimization.
19 70 0.101392647883 Henry Cohn, 2025, needs more optimization.
19 71 0.101456853396 Henry Cohn, 2025, needs more optimization.
19 72 0.102183669714 Henry Cohn, 2026, needs more optimization.
19 73 0.102201317334 Henry Cohn, 2026.
311⁢x2−22⁢x−1
19 74 0.104261701003 Henry Cohn, 2026, needs more optimization.
19 75 0.107816370386 Henry Cohn, 2026, needs more optimization.
19 76 0.111567748620 Henry Cohn, 2026, needs more optimization.
19 77 0.112842766161 Henry Cohn, 2026, needs more optimization.
19 89 0.112912613537 Henry Cohn, 2023.
167⁢x2−10⁢x−1
19 90 0.121308037796 Henry Cohn, 2024.
2809⁢x4−192⁢x3−86⁢x2+1
19 91 0.132272376899 Henry Cohn, 2026, needs more optimization.
19 92 0.134883034236 Henry Cohn, 2026, needs more optimization.
19 100 0.142857142858 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−1
19 102 0.142857142858 Henry Cohn, 2023, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−1
19 103 0.153836524069 Henry Cohn, 2026, needs more optimization.
19 105 0.155558023696 Henry Cohn, 2026, needs more optimization.
19 106 0.155560107315 Henry Cohn, 2026, needs more optimization.
19 107 0.155579742659 Henry Cohn, 2026, needs more optimization.
19 132 0.157894736843 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
19⁢x−3
19 133 0.168802199662 Henry Cohn, 2026, needs more optimization.
19 134 0.174620105379 Henry Cohn, 2026, needs more optimization.
19 135 0.177865614686 Henry Cohn, 2026, needs more optimization.
19 136 0.177874933883 Henry Cohn, 2026, needs more optimization.
19 137 0.177881887214 Henry Cohn, 2026, needs more optimization.
19 138 0.177905918343 Henry Cohn, 2026, needs more optimization.
19 139 0.178029612350 Henry Cohn, 2026, needs more optimization.
19 140 0.178176831448 Henry Cohn, 2026, needs more optimization.
19 141 0.178377871257 Henry Cohn, 2026, needs more optimization.
19 142 0.178808740741 Henry Cohn, 2026, needs more optimization.
19 143 0.179240702060 Henry Cohn, 2026, needs more optimization.
19 144 0.179754356322 Henry Cohn, 2026, needs more optimization.
19 145 0.180769687081 Henry Cohn, 2026, needs more optimization.
19 146 0.181639872413 Henry Cohn, 2026, needs more optimization.
19 147 0.182398746095 Henry Cohn, 2026, needs more optimization.
19 148 0.183369175231 Henry Cohn, 2026, needs more optimization.
19 149 0.183926699205 Henry Cohn, 2026, needs more optimization.
19 150 0.184646543856 Henry Cohn, 2026, needs more optimization.
19 151 0.186861702854 Henry Cohn, 2026, needs more optimization.
19 166 0.189189189190 Henry Cohn, 2026.
37⁢x−7
19 176 0.191919191920 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
99⁢x−19
19 177 0.193637369266 Henry Cohn, 2026, needs more optimization.
19 178 0.194663251791 Henry Cohn, 2026, needs more optimization.
19 179 0.195476943440 Henry Cohn, 2026, needs more optimization.
19 180 0.195821119732 Henry Cohn, 2026, needs more optimization.
19 181 0.198089979723 Henry Cohn, 2026, needs more optimization.
19 182 0.198331863069 Henry Cohn, 2026, needs more optimization.
19 183 0.199880167000 Henry Cohn, 2026, needs more optimization.
19 192 0.2 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−1
19 193 0.203357314610 Henry Cohn, 2026, needs more optimization.
19 194 0.205905415993 Henry Cohn, 2026, needs more optimization.
19 195 0.207110998407 Henry Cohn, 2026, needs more optimization.
19 196 0.208049605574 Henry Cohn, 2026, needs more optimization.
19 197 0.208693183226 Henry Cohn, 2026, needs more optimization.
19 198 0.209395754617 Henry Cohn, 2026, needs more optimization.
19 199 0.209808492233 Henry Cohn, 2026, needs more optimization.
19 200 0.210590908756 Henry Cohn, 2026, needs more optimization.
19 201 0.211119359176 Henry Cohn, 2026, needs more optimization.
19 202 0.211607234808 Henry Cohn, 2026, needs more optimization.
19 203 0.212023097503 Henry Cohn, 2026, needs more optimization.
19 204 0.212310398135 Henry Cohn, 2026, needs more optimization.
19 205 0.212686045465 Henry Cohn, 2026, needs more optimization.
19 206 0.212895490517 Henry Cohn, 2026, needs more optimization.
19 207 0.213597106797 Henry Cohn, 2026, needs more optimization.
19 208 0.214239466243 Henry Cohn, 2026, needs more optimization.
19 209 0.214710942014 Henry Cohn, 2026, needs more optimization.
19 210 0.215123194194 Henry Cohn, 2026, needs more optimization.
19 211 0.215406418624 Henry Cohn, 2026, needs more optimization.
19 212 0.215588913550 Henry Cohn, 2026, needs more optimization.
19 213 0.216096289422 Henry Cohn, 2026, needs more optimization.
19 214 0.216351824391 Henry Cohn, 2026, needs more optimization.
19 215 0.218058431888 Henry Cohn, 2026, needs more optimization.
19 216 0.219013599468 Henry Cohn, 2026, needs more optimization.
19 217 0.219774131015 Henry Cohn, 2026, needs more optimization.
19 218 0.220505258820 Henry Cohn, 2026, needs more optimization.
19 219 0.221099623902 Henry Cohn, 2026, needs more optimization.
19 240 0.230769230770 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
13⁢x−3
19 277 0.230769230770 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
13⁢x−3
19 291 0.238519274309 Henry Cohn, 2026, needs more optimization.
19 292 0.243289905986 Henry Cohn, 2026, needs more optimization.
19 293 0.244127472826 Henry Cohn, 2026, needs more optimization.
19 294 0.245709904195 Henry Cohn, 2026, needs more optimization.
19 297 0.246500410186 Henry Cohn, 2026, needs more optimization.
19 298 0.248395767298 Henry Cohn, 2026, needs more optimization.
19 299 0.248551711591 Henry Cohn, 2026, needs more optimization.
19 300 0.248940579476 Henry Cohn, 2026, needs more optimization.
19 301 0.249978686033 Henry Cohn, 2026, needs more optimization.
19 304 0.249991047942 Henry Cohn, 2026, needs more optimization.
19 307 0.249994992895 Henry Cohn, 2026, needs more optimization.
19 308 0.249995703148 Henry Cohn, 2026, needs more optimization.
19 310 0.250005325886 Henry Cohn, 2026, needs more optimization.
19 312 0.250025250933 Henry Cohn, 2026, needs more optimization.
19 314 0.250027040456 Henry Cohn, 2026, needs more optimization.
19 316 0.250040452200 Henry Cohn, 2026, needs more optimization.
19 318 0.250041457295 Henry Cohn, 2026, needs more optimization.
19 321 0.250043209609 Henry Cohn, 2026, needs more optimization.
19 322 0.250097646993 Henry Cohn, 2026, needs more optimization.
19 323 0.250124054478 Henry Cohn, 2026, needs more optimization.
19 324 0.250729997305 Henry Cohn, 2026, needs more optimization.
19 325 0.251181376933 Henry Cohn, 2026, needs more optimization.
19 326 0.261122073875 Orthogonal union of 324 points in 18 dimensions and 2 points in 1 dimension.
19 332 0.287398663717 Henry Cohn, 2026, needs more optimization.
19 340 0.287416145165 Henry Cohn, 2026, needs more optimization.
19 348 0.287449455963 Henry Cohn, 2026, needs more optimization.
19 356 0.287524600805 Henry Cohn, 2026, needs more optimization.
19 364 0.287656995428 Henry Cohn, 2026, needs more optimization.
19 372 0.287798049757 Henry Cohn, 2026, needs more optimization.
19 376 0.288078500644 Henry Cohn, 2026, needs more optimization.
19 380 0.288357058273 Henry Cohn, 2026, needs more optimization.
19 388 0.288704069518 Henry Cohn, 2026, needs more optimization.
19 396 0.289244031804 Henry Cohn, 2026, needs more optimization.
19 404 0.290065933177 Henry Cohn, 2026, needs more optimization.
19 408 0.290719405993 Henry Cohn, 2026, needs more optimization.
19 412 0.290774650598 Henry Cohn, 2026, needs more optimization.
19 415 0.291690435834 Henry Cohn, 2026, needs more optimization.
19 485 0.296296296297 Henry Cohn, 2025.
27⁢x−8
19 560 0.304347826087 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
23⁢x−7
19 576 0.304347826087 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
23⁢x−7
19 577 0.304507931848 Henry Cohn, 2026, needs more optimization.
19 578 0.304559376332 Henry Cohn, 2026, needs more optimization.
19 579 0.304610478353 Henry Cohn, 2026, needs more optimization.
19 580 0.304616094668 Henry Cohn, 2026, needs more optimization.
19 581 0.304638247229 Henry Cohn, 2026, needs more optimization.
19 582 0.304674048208 Henry Cohn, 2026, needs more optimization.
19 584 0.304688572506 Henry Cohn, 2026, needs more optimization.
19 585 0.304712559975 Henry Cohn, 2026, needs more optimization.
19 586 0.304732933650 Henry Cohn, 2026, needs more optimization.
19 588 0.304747554025 Henry Cohn, 2026, needs more optimization.
19 589 0.304768584912 Henry Cohn, 2026, needs more optimization.
19 590 0.304798319072 Henry Cohn, 2026, needs more optimization.
19 591 0.304807267890 Henry Cohn, 2026, needs more optimization.
19 592 0.304816887679 Henry Cohn, 2026, needs more optimization.
19 593 0.304850036313 Henry Cohn, 2025, needs more optimization.
19 594 0.304870068483 Henry Cohn, 2025, needs more optimization.
19 596 0.304882572546 Henry Cohn, 2026, needs more optimization.
19 597 0.304904010177 Henry Cohn, 2025, needs more optimization.
19 598 0.304914905451 Henry Cohn, 2025, needs more optimization.
19 600 0.304924768823 Henry Cohn, 2026, needs more optimization.
19 604 0.304954995080 Henry Cohn, 2026, needs more optimization.
19 605 0.304998577549 Henry Cohn, 2025, needs more optimization.
19 606 0.305007916218 Henry Cohn, 2026, needs more optimization.
19 607 0.305008902041 Henry Cohn, 2025, needs more optimization.
19 608 0.305013451984 Henry Cohn, 2026, needs more optimization.
19 609 0.305031662932 Henry Cohn, 2025, needs more optimization.
19 612 0.305031675525 Henry Cohn, 2026, needs more optimization.
19 613 0.305048594759 Henry Cohn, 2025, needs more optimization.
19 616 0.305050192359 Henry Cohn, 2026, needs more optimization.
19 617 0.305068555187 Henry Cohn, 2025, needs more optimization.
19 620 0.305081347021 Henry Cohn, 2026, needs more optimization.
19 624 0.305097417134 Henry Cohn, 2026, needs more optimization.
19 625 0.305114170876 Henry Cohn, 2025, needs more optimization.
19 628 0.305119407750 Henry Cohn, 2026, needs more optimization.
19 629 0.305137259572 Henry Cohn, 2025, needs more optimization.
19 630 0.305143351492 Henry Cohn, 2025, needs more optimization.
19 632 0.305145919737 Henry Cohn, 2026, needs more optimization.
19 633 0.305160018914 Henry Cohn, 2025, needs more optimization.
19 636 0.305161817320 Henry Cohn, 2026, needs more optimization.
19 640 0.305175574270 Henry Cohn, 2026, needs more optimization.
19 644 0.309227966944 Henry Cohn, 2026, needs more optimization.
19 646 0.309904355337 Henry Cohn, 2025, needs more optimization.
19 648 0.311072646970 Henry Cohn, 2026, needs more optimization.
19 649 0.312098563188 Henry Cohn, 2026, needs more optimization.
19 650 0.312098563493 Henry Cohn, 2026, needs more optimization.
19 651 0.312098563747 Henry Cohn, 2025, needs more optimization.
19 652 0.312302448986 Henry Cohn, 2026, needs more optimization.
19 656 0.313222186607 Henry Cohn, 2026, needs more optimization.
19 660 0.314243955461 Henry Cohn, 2026, needs more optimization.
19 664 0.315048124686 Henry Cohn, 2026, needs more optimization.
19 666 0.315489930454 Henry Cohn, 2026, needs more optimization.
19 896 0.333333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−1
19 897 0.339605417332 Henry Cohn, 2025, needs more optimization.
19 898 0.341321382896 Henry Cohn, 2026, needs more optimization.
19 899 0.342826411178 Henry Cohn, 2025, needs more optimization.
19 900 0.344190688570 Henry Cohn, 2026, needs more optimization.
19 901 0.345826645384 Henry Cohn, 2025, needs more optimization.
19 902 0.346196560527 Henry Cohn, 2026, needs more optimization.
19 903 0.347200185233 Henry Cohn, 2025, needs more optimization.
19 904 0.347511723865 Henry Cohn, 2026, needs more optimization.
19 905 0.348090774308 Henry Cohn, 2025, needs more optimization.
19 906 0.348488327193 Henry Cohn, 2026, needs more optimization.
19 907 0.349125653486 Henry Cohn, 2025, needs more optimization.
19 908 0.349379233183 Henry Cohn, 2026, needs more optimization.
19 909 0.349790733491 Henry Cohn, 2026, needs more optimization.
19 910 0.350078486751 Henry Cohn, 2026, needs more optimization.
19 911 0.350202781234 Henry Cohn, 2025, needs more optimization.
19 912 0.350921071750 Henry Cohn, 2026, needs more optimization.
19 913 0.351034600979 Henry Cohn, 2025, needs more optimization.
19 914 0.351442708251 Henry Cohn, 2025, needs more optimization.
19 915 0.351545937935 Henry Cohn, 2025, needs more optimization.
19 1024 0.368421052632 N. J. A. Sloane, S. M. Reddy, and C.-L. Chen, New binary codes, IEEE Trans. Inform. Theory 18 (1972), 503–510, doi:10.1109/tit.1972.1054833.
19⁢x−7
20 41 0.038815055717 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
6480⁢x3−400⁢x2−20⁢x+1
20 42 0.045454545455 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
22⁢x−1
20 43 0.050117159654 Henry Cohn, 2024.
6493504⁢x6+4442432⁢x5−359919⁢x4−90844⁢x3+13006⁢x2−588⁢x+9
20 44 0.051781487230 Henry Cohn, 2023.
20 45 0.053400898990 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
20 46 0.053968966531 Henry Cohn, 2025.
20 47 0.053993355922 Henry Cohn, 2023.
120⁢x2−25⁢x+1
20 48 0.055838151510 Henry Cohn, 2023.
464⁢x2−8⁢x−1
20 49 0.060513303142 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
20 50 0.063702950432 Henry Cohn, 2025.
20 56* 0.066666666667 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
15⁢x−1
20 60 0.076923076924 Kissing configuration of 77 points in 21 dimensions.
13⁢x−1
20 63 0.081967213115 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
61⁢x−5
20 64 0.087282748333 Henry Cohn, 2026.
20 65 0.087640553690 Henry Cohn, 2026, needs more optimization.
20 66 0.089602007877 Henry Cohn, 2026, needs more optimization.
20 67 0.095918257385 Henry Cohn, 2026, needs more optimization.
20 68 0.097744099611 Henry Cohn, 2025, needs more optimization.
20 81 0.1 A. E. Brouwer and W. H. Haemers, Structure and uniqueness of the (81,20,1,6) strongly regular graph, Discrete Math. 106/107 (1992), 77–82, doi:10.1016/0012-365X(92)90532-K.
10⁢x−1
20 82 0.111111111112 Henry Cohn, 2026.
9⁢x−1
20 84 0.112895349963 Henry Cohn, 2025, needs more optimization.
20 85 0.112902505500 Henry Cohn, 2025, needs more optimization.
20 87 0.112912074804 Henry Cohn, 2025, needs more optimization.
20 88 0.112912612812 Henry Cohn, 2025, needs more optimization.
20 89 0.112912613185 Henry Cohn, 2025, needs more optimization.
20 92 0.112912613537 Henry Cohn, 2025.
167⁢x2−10⁢x−1
20 93 0.121893957808 Henry Cohn, 2026, needs more optimization.
20 105 0.125 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
8⁢x−1
20 106 0.136915269074 Henry Cohn, 2026, needs more optimization.
20 120 0.142857142858 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
7⁢x−1
20 124 0.145853791081 Henry Cohn, 2026, needs more optimization.
20 125 0.147670835579 Henry Cohn, 2026, needs more optimization.
20 126 0.149831609589 Henry Cohn, 2026, needs more optimization.
20 127 0.150090306704 Henry Cohn, 2026, needs more optimization.
20 128 0.150091864275 Henry Cohn, 2026, needs more optimization.
20 129 0.150493364755 Henry Cohn, 2026, needs more optimization.
20 130 0.150610322438 Henry Cohn, 2026, needs more optimization.
20 132 0.150697836381 Henry Cohn, 2026, needs more optimization.
20 133 0.151453018405 Henry Cohn, 2026, needs more optimization.
20 135 0.151505609414 Henry Cohn, 2026, needs more optimization.
20 136 0.151506098385 Henry Cohn, 2026, needs more optimization.
20 137 0.153202651097 Henry Cohn, 2026, needs more optimization.
20 138 0.154440405466 Henry Cohn, 2026, needs more optimization.
20 139 0.155171111576 Henry Cohn, 2026, needs more optimization.
20 140 0.156027125137 Henry Cohn, 2026, needs more optimization.
20 141 0.157502608513 Henry Cohn, 2025, needs more optimization.
20 142 0.161809087535 Henry Cohn, 2026, needs more optimization.
20 170 0.166666666667 E. Bannai and N. J. A. Sloane, Uniqueness of certain spherical codes, Canadian J. Math. 33 (1981), 437–449, doi:10.4153/CJM-1981-038-7.
6⁢x−1
20 171 0.181540268775 Henry Cohn, 2026, needs more optimization.
20 172 0.189109200345 Henry Cohn, 2026, needs more optimization.
20 178 0.189194333371 Henry Cohn, 2026, needs more optimization.
20 180 0.189195228428 Henry Cohn, 2026, needs more optimization.
20 184 0.189196499350 Henry Cohn, 2026, needs more optimization.
20 185 0.189200617046 Henry Cohn, 2026, needs more optimization.
20 187 0.189201160915 Henry Cohn, 2026, needs more optimization.
20 188 0.189203060702 Henry Cohn, 2026, needs more optimization.
20 189 0.190724637857 Henry Cohn, 2026, needs more optimization.
20 190 0.192184863175 Henry Cohn, 2026, needs more optimization.
20 231 0.192307692308 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
26⁢x−5
20 256 0.2 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
5⁢x−1
20 262 0.208386801326 Henry Cohn, 2026, needs more optimization.
20 263 0.208856371119 Henry Cohn, 2026, needs more optimization.
20 264 0.208862423530 Henry Cohn, 2026, needs more optimization.
20 265 0.215340499599 Henry Cohn, 2026, needs more optimization.
20 266 0.218839013131 Henry Cohn, 2026, needs more optimization.
20 267 0.218843434758 Henry Cohn, 2026, needs more optimization.
20 268 0.218846640460 Henry Cohn, 2026, needs more optimization.
20 269 0.218893426482 Henry Cohn, 2026, needs more optimization.
20 270 0.218896677981 Henry Cohn, 2026, needs more optimization.
20 271 0.218907991187 Henry Cohn, 2026, needs more optimization.
20 272 0.218911333577 Henry Cohn, 2026, needs more optimization.
20 273 0.218913094158 Henry Cohn, 2026, needs more optimization.
20 274 0.218917980505 Henry Cohn, 2026, needs more optimization.
20 275 0.218926740860 Henry Cohn, 2026, needs more optimization.
20 276 0.218928141029 Henry Cohn, 2026, needs more optimization.
20 277 0.218933485739 Henry Cohn, 2026, needs more optimization.
20 278 0.218935918304 Henry Cohn, 2026, needs more optimization.
20 279 0.218938293587 Henry Cohn, 2026, needs more optimization.
20 294 0.220695461526 Henry Cohn, 2024, needs more optimization.
20 301 0.222222222223 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−2
20 322 0.222222222223 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−2
20 378 0.236363636364 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
55⁢x−13
20 405 0.25 C. Ma, T. T. Zhaowei, P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
4⁢x−1
20 406 0.262180653313 Henry Cohn, 2026, needs more optimization.
20 473 0.266666666667 Henry Cohn, 2025.
15⁢x−4
20 474 0.269878877064 Henry Cohn, 2026, needs more optimization.
20 475 0.271304137415 Henry Cohn, 2025, needs more optimization.
20 476 0.272622512553 Henry Cohn, 2026, needs more optimization.
20 477 0.273459280230 Henry Cohn, 2025, needs more optimization.
20 478 0.274387603276 Henry Cohn, 2025, needs more optimization.
20 479 0.275200367871 Henry Cohn, 2025, needs more optimization.
20 480 0.275966924004 Henry Cohn, 2026, needs more optimization.
20 488 0.276469909920 Henry Cohn, 2026, needs more optimization.
20 492 0.278204522843 Henry Cohn, 2026, needs more optimization.
20 496 0.278298282200 Henry Cohn, 2026, needs more optimization.
20 497 0.281336900131 Henry Cohn, 2025, needs more optimization.
20 498 0.281346725928 Henry Cohn, 2026, needs more optimization.
20 499 0.281346754647 Henry Cohn, 2025, needs more optimization.
20 500 0.281348261555 Henry Cohn, 2025, needs more optimization.
20 503 0.281393107933 Henry Cohn, 2025, needs more optimization.
20 504 0.283650277827 Henry Cohn, 2026, needs more optimization.
20 508 0.285343377207 Henry Cohn, 2026, needs more optimization.
20 511 0.285651857828 Henry Cohn, 2025, needs more optimization.
20 516 0.288364124534 Henry Cohn, 2026, needs more optimization.
20 520 0.288372970609 Henry Cohn, 2026, needs more optimization.
20 521 0.289404389705 Henry Cohn, 2026, needs more optimization.
20 544 0.289726812929 Henry Cohn, 2026, needs more optimization.
20 548 0.289726813349 Henry Cohn, 2026, needs more optimization.
20 549 0.289734511943 Henry Cohn, 2025, needs more optimization.
20 550 0.289735107894 Henry Cohn, 2025, needs more optimization.
20 552 0.289765170476 Henry Cohn, 2026, needs more optimization.
20 673 0.304347826087 Henry Cohn, 2025.
23⁢x−7
20 676 0.304396956509 Henry Cohn, 2025, needs more optimization.
20 678 0.304400569629 Henry Cohn, 2025, needs more optimization.
20 679 0.304412508599 Henry Cohn, 2025, needs more optimization.
20 896 0.311475409837 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
61⁢x−19
20 897 0.312190960644 Henry Cohn, 2025, needs more optimization.
20 898 0.312346245971 Henry Cohn, 2026, needs more optimization.
20 899 0.312531816974 Henry Cohn, 2025, needs more optimization.
20 900 0.312540011762 Henry Cohn, 2026, needs more optimization.
20 901 0.312720092892 Henry Cohn, 2025, needs more optimization.
20 902 0.312829711046 Henry Cohn, 2026, needs more optimization.
20 903 0.312959756948 Henry Cohn, 2025, needs more optimization.
20 904 0.312985013976 Henry Cohn, 2026, needs more optimization.
20 905 0.313030006626 Henry Cohn, 2025, needs more optimization.
20 906 0.313124201212 Henry Cohn, 2026, needs more optimization.
20 907 0.313177804356 Henry Cohn, 2025, needs more optimization.
20 908 0.313269275702 Henry Cohn, 2026, needs more optimization.
20 909 0.313319621737 Henry Cohn, 2025, needs more optimization.
20 910 0.313362748697 Henry Cohn, 2026, needs more optimization.
20 911 0.313437876546 Henry Cohn, 2025, needs more optimization.
20 912 0.313458851296 Henry Cohn, 2026, needs more optimization.
20 913 0.313515019568 Henry Cohn, 2025, needs more optimization.
20 914 0.313570152004 Henry Cohn, 2026, needs more optimization.
20 915 0.313687412324 Henry Cohn, 2025, needs more optimization.
20 916 0.313689185245 Henry Cohn, 2026, needs more optimization.
20 917 0.313742181219 Henry Cohn, 2025, needs more optimization.
20 918 0.313767938376 Henry Cohn, 2026, needs more optimization.
20 920 0.313821753717 Henry Cohn, 2026, needs more optimization.
20 921 0.313871643206 Henry Cohn, 2025, needs more optimization.
20 922 0.313884239983 Henry Cohn, 2026, needs more optimization.
20 924 0.313896470232 Henry Cohn, 2026, needs more optimization.
20 925 0.313926649291 Henry Cohn, 2025, needs more optimization.
20 926 0.313932743468 Henry Cohn, 2026, needs more optimization.
20 928 0.313987096650 Henry Cohn, 2026, needs more optimization.
20 929 0.314045700687 Henry Cohn, 2025, needs more optimization.
20 930 0.314060382132 Henry Cohn, 2026, needs more optimization.
20 932 0.314105414716 Henry Cohn, 2026, needs more optimization.
20 934 0.314138377266 Henry Cohn, 2026, needs more optimization.
20 936 0.314148192896 Henry Cohn, 2026, needs more optimization.
20 938 0.314173973895 Henry Cohn, 2026, needs more optimization.
20 939 0.314212488531 Henry Cohn, 2025, needs more optimization.
20 940 0.314247841153 Henry Cohn, 2026, needs more optimization.
20 942 0.314280076412 Henry Cohn, 2026, needs more optimization.
20 944 0.314310558267 Henry Cohn, 2026, needs more optimization.
20 946 0.314337699210 Henry Cohn, 2026, needs more optimization.
20 947 0.314377623395 Henry Cohn, 2025, needs more optimization.
20 948 0.314389395166 Henry Cohn, 2026, needs more optimization.
20 949 0.314424194227 Henry Cohn, 2025, needs more optimization.
20 950 0.314426869619 Henry Cohn, 2026, needs more optimization.
20 952 0.314458294723 Henry Cohn, 2026, needs more optimization.
20 953 0.314484691487 Henry Cohn, 2025, needs more optimization.
20 954 0.314500912913 Henry Cohn, 2026, needs more optimization.
20 955 0.314549253350 Henry Cohn, 2025, needs more optimization.
20 956 0.314553955096 Henry Cohn, 2026, needs more optimization.
20 958 0.314580635862 Henry Cohn, 2026, needs more optimization.
20 960 0.314608007053 Henry Cohn, 2026, needs more optimization.
20 961 0.314636423852 Henry Cohn, 2025, needs more optimization.
20 962 0.314640337377 Henry Cohn, 2026, needs more optimization.
20 964 0.314653666340 Henry Cohn, 2026, needs more optimization.
20 966 0.314668360655 Henry Cohn, 2026, needs more optimization.
20 968 0.314691494481 Henry Cohn, 2026, needs more optimization.
20 970 0.314701383628 Henry Cohn, 2026, needs more optimization.
20 972 0.316635841942 Henry Cohn, 2026, needs more optimization.
20 974 0.316637012300 Henry Cohn, 2026, needs more optimization.
20 976 0.316637268930 Henry Cohn, 2026, needs more optimization.
20 977 0.316731825153 Henry Cohn, 2025, needs more optimization.
20 978 0.317291630840 Henry Cohn, 2026, needs more optimization.
20 980 0.318163805803 Henry Cohn, 2026, needs more optimization.
20 982 0.318175051037 Henry Cohn, 2026, needs more optimization.
20 984 0.318183545207 Henry Cohn, 2026, needs more optimization.
20 988 0.318200273204 Henry Cohn, 2026, needs more optimization.
20 989 0.318314238796 Henry Cohn, 2025, needs more optimization.
20 990 0.318498649335 Henry Cohn, 2026, needs more optimization.
20 991 0.319493547827 Henry Cohn, 2025, needs more optimization.
20 992 0.319662706947 Henry Cohn, 2026, needs more optimization.
20 994 0.320421726048 Henry Cohn, 2026, needs more optimization.
20 996 0.321277826314 Henry Cohn, 2026, needs more optimization.
20 998 0.321868831705 Henry Cohn, 2026, needs more optimization.
20 1002 0.322170877535 Henry Cohn, 2026, needs more optimization.
20 1004 0.323142177678 Henry Cohn, 2026, needs more optimization.
20 1006 0.323142292848 Henry Cohn, 2026, needs more optimization.
20 1008 0.323233914732 Henry Cohn, 2026, needs more optimization.
20 1010 0.323535144301 Henry Cohn, 2026, needs more optimization.
20 1012 0.323933408162 Henry Cohn, 2026, needs more optimization.
20 1014 0.323934953375 Henry Cohn, 2026, needs more optimization.
20 1015 0.323956619698 Henry Cohn, 2025, needs more optimization.
20 1016 0.324031372969 Henry Cohn, 2026, needs more optimization.
20 1017 0.324054978602 Henry Cohn, 2025, needs more optimization.
20 1018 0.324162313124 Henry Cohn, 2026, needs more optimization.
20 1020 0.324162583394 Henry Cohn, 2026, needs more optimization.
20 1022 0.324253213675 Henry Cohn, 2026, needs more optimization.
20 1024 0.324776552083 Henry Cohn, 2026, needs more optimization.
21 43 0.037145782135 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7581⁢x3−441⁢x2−21⁢x+1
21 44 0.043532808199 Henry Cohn, 2023.
21 50* 0.047619047620 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
21⁢x−1
21 51 0.058803648698 Henry Cohn, 2024.
21 52 0.062643510087 Henry Cohn, 2023.
21 53 0.066665620363 Henry Cohn, 2025.
21 54 0.066665850459 Henry Cohn, 2025.
21 55 0.066666409280 Henry Cohn, 2025.
21 56 0.066666653891 Henry Cohn, 2025, needs more optimization.
21 57 0.066666662289 Henry Cohn, 2025, needs more optimization.
21 58 0.066666666337 Henry Cohn, 2025, needs more optimization.
21 59 0.072019011748 Henry Cohn, 2025.
21 60 0.074662292991 Henry Cohn, 2026.
21 61 0.076923073145 Henry Cohn, 2025, needs more optimization.
21 62 0.076923075369 Henry Cohn, 2025, needs more optimization.
21 63 0.078689325834 Henry Cohn, 2026.
9⁢x2+12⁢x−1
21 64 0.080216778694 Henry Cohn, 2026.
21 65 0.081966984796 Henry Cohn, 2025, needs more optimization.
21 77* 0.083333333334 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
12⁢x−1
21 78 0.093247656079 Henry Cohn, 2026, needs more optimization.
21 81 0.093297851019 Henry Cohn, 2026, needs more optimization.
21 82 0.093297851020 Henry Cohn, 2026, needs more optimization.
21 83 0.095616261103 Henry Cohn, 2026, needs more optimization.
21 84 0.096120290871 Henry Cohn, 2026, needs more optimization.
21 85 0.097702080335 Henry Cohn, 2026, needs more optimization.
21 86 0.104649382380 Henry Cohn, 2026, needs more optimization.
21 87 0.107536753613 Henry Cohn, 2026, needs more optimization.
21 88 0.108040226878 Henry Cohn, 2026, needs more optimization.
21 89 0.108846463758 Henry Cohn, 2026, needs more optimization.
21 90 0.110085419958 Henry Cohn, 2026, needs more optimization.
21 91 0.110089945291 Henry Cohn, 2026, needs more optimization.
21 92 0.110758056129 Henry Cohn, 2026, needs more optimization.
21 93 0.110771839137 Henry Cohn, 2026, needs more optimization.
21 112* 0.111111111112 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
9⁢x−1
21 113 0.127363959721 Henry Cohn, 2026, needs more optimization.
21 119 0.131782945737 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
129⁢x−17
21 122 0.139354052717 Henry Cohn, 2026, needs more optimization.
21 123 0.139446357525 Henry Cohn, 2026, needs more optimization.
21 124 0.140535785430 Henry Cohn, 2026, needs more optimization.
21 162* 0.142857142858 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
7⁢x−1
21 163 0.153926281049 Henry Cohn, 2026, needs more optimization.
21 164 0.160794343575 Henry Cohn, 2026, needs more optimization.
21 198 0.161904761905 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
105⁢x−17
21 199 0.172187000258 Henry Cohn, 2026, needs more optimization.
21 200 0.179136630980 Henry Cohn, 2026, needs more optimization.
21 201 0.183755880676 Henry Cohn, 2026, needs more optimization.
21 202 0.185633668172 Henry Cohn, 2026, needs more optimization.
21 203 0.186150112756 Henry Cohn, 2026, needs more optimization.
21 204 0.186524056153 Henry Cohn, 2026, needs more optimization.
21 205 0.188124712243 Henry Cohn, 2026, needs more optimization.
21 206 0.188766063918 Henry Cohn, 2026, needs more optimization.
21 207 0.188942886780 Henry Cohn, 2026, needs more optimization.
21 208 0.189175863014 Henry Cohn, 2026, needs more optimization.
21 210 0.189189189190 Kissing configuration of 529 points in 22 dimensions from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
37⁢x−7
21 225 0.189189189190 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
37⁢x−7
21 233 0.192307692308 Code with 231 points in 20 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
26⁢x−5
21 336 0.2 E. Bannai and N. J. A. Sloane, Uniqueness of certain spherical codes, Canadian J. Math. 33 (1981), 437–449, doi:10.4153/CJM-1981-038-7.
5⁢x−1
21 345 0.230818230927 Henry Cohn, 2026, needs more optimization.
21 353 0.230819078355 Henry Cohn, 2026, needs more optimization.
21 371 0.230820117549 Henry Cohn, 2026, needs more optimization.
21 374 0.230820493211 Henry Cohn, 2026, needs more optimization.
21 375 0.230828419531 Henry Cohn, 2026, needs more optimization.
21 380 0.230829007825 Henry Cohn, 2026, needs more optimization.
21 381 0.230829256256 Henry Cohn, 2026, needs more optimization.
21 388 0.230893614344 Henry Cohn, 2026, needs more optimization.
21 554 0.238095238096 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
21⁢x−5
21 660 0.266666666667 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
15⁢x−4
21 716 0.272727272728 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11⁢x−3
21 1024 0.311475409837 Henry Cohn, 2025.
61⁢x−19
22 45 0.035618974680 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
8800⁢x3−484⁢x2−22⁢x+1
22 46 0.041709010751 Henry Cohn, 2026.
22 47 0.046962270332 Henry Cohn, 2026.
22 48 0.047524915294 Henry Cohn, 2025, continuous family of codes without rattlers.
64⁢x2+18⁢x−1
22 49 0.047603596837 Henry Cohn, 2025, needs more optimization.
22 50 0.047618606209 Henry Cohn, 2025, needs more optimization.
22 52 0.047619047316 Henry Cohn, 2025, needs more optimization.
22 53 0.057560345703 Henry Cohn, 2024.
22 54 0.060108874148 Henry Cohn, 2025.
22 55 0.064358164597 Henry Cohn, 2026, needs more optimization.
22 56 0.066598164965 Henry Cohn, 2026, needs more optimization.
22 57 0.066647961036 Henry Cohn, 2026, needs more optimization.
22 59 0.066664590405 Henry Cohn, 2026, needs more optimization.
22 60 0.066664720886 Henry Cohn, 2026, needs more optimization.
22 61 0.069653549396 Henry Cohn, 2026, needs more optimization.
22 62 0.071702992839 Henry Cohn, 2026, needs more optimization.
22 64 0.076920313939 Henry Cohn, 2025, needs more optimization.
22 65 0.076924075556 Henry Cohn, 2026, needs more optimization.
22 66 0.078243584927 Henry Cohn, 2026, needs more optimization.
22 67 0.079295799194 Henry Cohn, 2026, needs more optimization.
22 68 0.080927905685 Henry Cohn, 2026, needs more optimization.
22 69 0.083023892084 Henry Cohn, 2026, needs more optimization.
22 70 0.083309827283 Henry Cohn, 2025, needs more optimization.
22 71 0.083331871272 Henry Cohn, 2025, needs more optimization.
22 72 0.083333305431 Henry Cohn, 2025, needs more optimization.
22 73 0.083333332773 Henry Cohn, 2025, needs more optimization.
22 79 0.083333333334 Code with 77 points in 21 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
12⁢x−1
22 80 0.086876541555 Henry Cohn, 2026, needs more optimization.
22 100* 0.090909090910 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
11⁢x−1
22 101 0.109433688341 Henry Cohn, 2026, needs more optimization.
22 114 0.111111111112 Code with 112 points in 21 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−1
22 115 0.112789665003 Henry Cohn, 2026.
68⁢x2−52⁢x+5
22 116 0.121319631223 Henry Cohn, 2026, needs more optimization.
22 117 0.122811460191 Henry Cohn, 2026, needs more optimization.
22 118 0.130947195767 Henry Cohn, 2026, needs more optimization.
22 121 0.131782945737 Code with 119 points in 21 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
129⁢x−17
22 126 0.131782945737 Henry Cohn, 2026.
129⁢x−17
22 136 0.135135135136 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
37⁢x−5
22 141 0.135135135136 Henry Cohn, 2026.
37⁢x−5
22 142 0.135581434330 Henry Cohn, 2026, needs more optimization.
22 143 0.138390129411 Henry Cohn, 2026, needs more optimization.
22 144 0.139626978555 Henry Cohn, 2026, needs more optimization.
22 164 0.142857142858 Code with 162 points in 21 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−1
22 166 0.142857142858 Henry Cohn, 2026.
7⁢x−1
22 167 0.150694419400 Henry Cohn, 2026, needs more optimization.
22 168 0.155185167736 Henry Cohn, 2026, needs more optimization.
22 169 0.159348029498 Henry Cohn, 2026, needs more optimization.
22 170 0.160003758433 Henry Cohn, 2026, needs more optimization.
22 171 0.160006219198 Henry Cohn, 2026, needs more optimization.
22 172 0.160020705989 Henry Cohn, 2026, needs more optimization.
22 173 0.160450024489 Henry Cohn, 2026, needs more optimization.
22 174 0.161685787951 Henry Cohn, 2026, needs more optimization.
22 200 0.161904761905 Code with 198 points in 21 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
105⁢x−17
22 201 0.161904762057 Henry Cohn, 2026, needs more optimization.
22 202 0.161908900522 Henry Cohn, 2026, needs more optimization.
22 203 0.165621390319 Henry Cohn, 2026, needs more optimization.
22 275* 0.166666666667 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
6⁢x−1
22 338 0.2 Code with 336 points in 21 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−1
22 428 0.209817070618 Henry Cohn, 2026, needs more optimization.
22 429 0.209819211160 Henry Cohn, 2026, needs more optimization.
22 430 0.209819211247 Henry Cohn, 2026, needs more optimization.
22 432 0.212433779378 Henry Cohn, 2026, needs more optimization.
22 433 0.212503875731 Henry Cohn, 2026, needs more optimization.
22 436 0.212565135786 Henry Cohn, 2026, needs more optimization.
22 437 0.212635538515 Henry Cohn, 2026, needs more optimization.
22 451 0.212654836504 Henry Cohn, 2026, needs more optimization.
22 484 0.229650348229 Henry Cohn, 2026, needs more optimization.
22 485 0.229651854557 Henry Cohn, 2026, needs more optimization.
22 504 0.229926564994 Henry Cohn, 2026, needs more optimization.
22 505 0.229927684818 Henry Cohn, 2025, needs more optimization.
22 506 0.231141363150 Henry Cohn, 2026, needs more optimization.
22 529 0.233333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
30⁢x−7
22 556 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 2 points in 1 dimension.
21⁢x−5
22 891* 0.25 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
4⁢x−1
22 1024 0.272727272728 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
11⁢x−3
23 47 0.034216857253 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
10143⁢x3−529⁢x2−23⁢x+1
23 48 0.040044233015 Henry Cohn, 2025.
23 49 0.045954913455 Henry Cohn, 2026.
23 50 0.046749604258 Henry Cohn, 2025, continuous family of codes without rattlers.
713⁢x3+215⁢x2−33⁢x+1
23 51 0.047343032480 Henry Cohn, 2026, needs more optimization.
23 52 0.047477902142 Henry Cohn, 2026, needs more optimization.
23 53 0.047609748527 Henry Cohn, 2024, needs more optimization.
23 54 0.047609798559 Henry Cohn, 2024, needs more optimization.
23 55 0.055674420072 Henry Cohn, 2024.
23 56 0.057275984127 Henry Cohn, 2025.
23 57 0.061654365426 Ilmari Vahteristo, 2026.
23 58 0.064515997905 Henry Cohn, 2026, needs more optimization.
23 59 0.066320745246 Henry Cohn, 2026, needs more optimization.
23 60 0.066528798193 Henry Cohn, 2026, needs more optimization.
23 61 0.066599568077 Henry Cohn, 2025, needs more optimization.
23 62 0.066599790838 Henry Cohn, 2025, needs more optimization.
23 63 0.067250816631 Henry Cohn, 2026, needs more optimization.
23 64 0.069716146304 Henry Cohn, 2026, needs more optimization.
23 65 0.073273148299 Henry Cohn, 2026, needs more optimization.
23 66 0.076830145449 Henry Cohn, 2026, needs more optimization.
23 67 0.076896812052 Henry Cohn, 2026, needs more optimization.
23 68 0.076898475206 Henry Cohn, 2026, needs more optimization.
23 69 0.077673812021 Henry Cohn, 2026, needs more optimization.
23 70 0.077985696760 Henry Cohn, 2026, needs more optimization.
23 71 0.079646217867 Henry Cohn, 2026, needs more optimization.
23 72 0.080582742027 Henry Cohn, 2026, needs more optimization.
23 73 0.082853645940 Henry Cohn, 2026, needs more optimization.
23 81 0.083333222004 Henry Cohn, 2025, needs more optimization.
23 82 0.083397112292 Henry Cohn, 2026, needs more optimization.
23 83 0.087449050695 Henry Cohn, 2026, needs more optimization.
23 84 0.090623839956 Henry Cohn, 2026, needs more optimization.
23 102 0.090909090910 Code with 100 points in 22 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11⁢x−1
23 103 0.094789393423 Henry Cohn, 2026.
67⁢x2−38⁢x+3
23 104 0.103889056804 Henry Cohn, 2026, needs more optimization.
23 116 0.111111109788 Henry Cohn, 2025, needs more optimization.
23 117 0.111124873982 Henry Cohn, 2026, needs more optimization.
23 118 0.114841775567 Henry Cohn, 2026, needs more optimization.
23 119 0.118704727684 Henry Cohn, 2026, needs more optimization.
23 120 0.121176526071 Henry Cohn, 2026, needs more optimization.
23 121 0.127647601521 Henry Cohn, 2026, needs more optimization.
23 122 0.130976777455 Henry Cohn, 2026, needs more optimization.
23 123 0.131779371379 Henry Cohn, 2025, needs more optimization.
23 128 0.131782945737 Orthogonal union of 126 points in 22 dimensions and 2 points in 1 dimension.
129⁢x−17
23 129 0.131787572852 Henry Cohn, 2026, needs more optimization.
23 130 0.131807435199 Henry Cohn, 2026, needs more optimization.
23 131 0.132303348888 Henry Cohn, 2026, needs more optimization.
23 132 0.134434136145 Henry Cohn, 2026, needs more optimization.
23 133 0.134909146276 Henry Cohn, 2026, needs more optimization.
23 138 0.135135135136 Code with 136 points in 22 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
37⁢x−5
23 147 0.135135135136 Henry Cohn, 2026.
37⁢x−5
23 148 0.136242492508 Henry Cohn, 2026, needs more optimization.
23 166 0.142857142858 Code with 164 points in 22 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−1
23 168 0.142857142858 Orthogonal union of 166 points in 22 dimensions and 2 points in 1 dimension.
7⁢x−1
23 170 0.142865346672 Henry Cohn, 2026, needs more optimization.
23 171 0.145731812776 Henry Cohn, 2026, needs more optimization.
23 172 0.146954878624 Henry Cohn, 2026, needs more optimization.
23 173 0.152684286153 Henry Cohn, 2026, needs more optimization.
23 174 0.155974636661 Henry Cohn, 2026, needs more optimization.
23 176 0.155974894065 Henry Cohn, 2026, needs more optimization.
23 177 0.158025881371 Henry Cohn, 2026, needs more optimization.
23 178 0.158819363116 Henry Cohn, 2026, needs more optimization.
23 179 0.160896335848 Henry Cohn, 2026, needs more optimization.
23 180 0.161336568901 Henry Cohn, 2026, needs more optimization.
23 202 0.161904761905 Code with 200 points in 22 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
105⁢x−17
23 203 0.161904762057 Orthogonal union of 201 points in 22 dimensions and 2 points in 1 dimension.
23 204 0.161908900522 Orthogonal union of 202 points in 22 dimensions and 2 points in 1 dimension.
23 205 0.161916902504 Henry Cohn, 2026, needs more optimization.
23 206 0.161927906175 Henry Cohn, 2026, needs more optimization.
23 207 0.162021926619 Henry Cohn, 2026, needs more optimization.
23 208 0.162490774137 Henry Cohn, 2026, needs more optimization.
23 209 0.165115669110 Henry Cohn, 2026, needs more optimization.
23 210 0.165853091046 Henry Cohn, 2026, needs more optimization.
23 211 0.165853091117 Henry Cohn, 2026, needs more optimization.
23 212 0.166417206769 Henry Cohn, 2026, needs more optimization.
23 277 0.166666666667 Code with 275 points in 22 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
6⁢x−1
23 279 0.171408036565 Henry Cohn, 2026, needs more optimization.
23 281 0.181918567390 Henry Cohn, 2026, needs more optimization.
23 283 0.183988535621 Henry Cohn, 2026, needs more optimization.
23 284 0.188519179676 Henry Cohn, 2026, needs more optimization.
23 285 0.188985112883 Henry Cohn, 2026, needs more optimization.
23 286 0.189266323919 Henry Cohn, 2026, needs more optimization.
23 288 0.189442338755 Henry Cohn, 2026, needs more optimization.
23 289 0.189508988656 Henry Cohn, 2026, needs more optimization.
23 291 0.198557992135 Henry Cohn, 2026, needs more optimization.
23 292 0.198580566782 Henry Cohn, 2026, needs more optimization.
23 293 0.199477525427 Henry Cohn, 2026, needs more optimization.
23 294 0.199491986979 Henry Cohn, 2026, needs more optimization.
23 295 0.199495707192 Henry Cohn, 2026, needs more optimization.
23 552* 0.2 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
5⁢x−1
23 558 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 4 points in 2 dimensions.
21⁢x−5
23 564 0.242347692504 Henry Cohn, 2026, needs more optimization.
23 568 0.243318196393 Henry Cohn, 2026, needs more optimization.
23 572 0.243350935121 Henry Cohn, 2026, needs more optimization.
23 893 0.25 Orthogonal union of 891 points in 22 dimensions and 2 points in 1 dimension.
4⁢x−1
23 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
23 4600* 0.333333333334 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
3⁢x−1
24 49 0.032924519945 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11616⁢x3−576⁢x2−24⁢x+1
24 50 0.038461538462 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
26⁢x−1
24 51 0.045537713846 Henry Cohn, 2025.
24 52 0.046377212908 Henry Cohn, 2025.
24 53 0.046712202497 Henry Cohn, 2025.
24 54 0.047284571428 Henry Cohn, 2025.
24 55 0.047381601960 Henry Cohn, 2024.
24 56 0.047563043071 Henry Cohn, 2024, needs more optimization.
24 57 0.053295300110 Ilmari Vahteristo, 2026.
24 58 0.054403503474 Henry Cohn, 2025.
24 59 0.057903810057 Henry Cohn, 2026.
24 60 0.061562313320 Henry Cohn, 2026, needs more optimization.
24 61 0.064814981405 Henry Cohn, 2026, needs more optimization.
24 62 0.065853017142 Henry Cohn, 2026, needs more optimization.
24 63 0.065859031114 Henry Cohn, 2026, needs more optimization.
24 64 0.065897911729 Henry Cohn, 2026, needs more optimization.
24 65 0.066587691116 Henry Cohn, 2026, needs more optimization.
24 66 0.068180518582 Henry Cohn, 2026, needs more optimization.
24 67 0.070763242144 Henry Cohn, 2026, needs more optimization.
24 68 0.072116568748 Henry Cohn, 2026, needs more optimization.
24 69 0.073247208276 Henry Cohn, 2026, needs more optimization.
24 70 0.076553865233 Henry Cohn, 2026, needs more optimization.
24 71 0.076921821053 Henry Cohn, 2026, needs more optimization.
24 72 0.077496905631 Henry Cohn, 2026, needs more optimization.
24 73 0.077887425403 Henry Cohn, 2026, needs more optimization.
24 74 0.077908692840 Henry Cohn, 2026, needs more optimization.
24 75 0.078600884756 Henry Cohn, 2026, needs more optimization.
24 76 0.078850062000 Henry Cohn, 2026, needs more optimization.
24 77 0.081790897066 Henry Cohn, 2026, needs more optimization.
24 78 0.082774182084 Henry Cohn, 2026, needs more optimization.
24 79 0.083297994991 Henry Cohn, 2026, needs more optimization.
24 80 0.083320095951 Henry Cohn, 2025, needs more optimization.
24 83 0.083320171859 Henry Cohn, 2025, needs more optimization.
24 84 0.083335156567 Henry Cohn, 2026, needs more optimization.
24 85 0.083335338109 Henry Cohn, 2026, needs more optimization.
24 86 0.086447948297 Henry Cohn, 2026, needs more optimization.
24 87 0.088167102736 Henry Cohn, 2026, needs more optimization.
24 88 0.089937149505 Henry Cohn, 2026, needs more optimization.
24 89 0.090291024770 Henry Cohn, 2026, needs more optimization.
24 90 0.090743696895 Henry Cohn, 2026, needs more optimization.
24 91 0.090834171392 Henry Cohn, 2026, needs more optimization.
24 92 0.090886623151 Henry Cohn, 2026, needs more optimization.
24 104 0.090909090666 Henry Cohn, 2025, needs more optimization.
24 105 0.091535358779 Henry Cohn, 2026, needs more optimization.
24 106 0.095288691538 Henry Cohn, 2026, needs more optimization.
24 107 0.102478292355 Henry Cohn, 2026, needs more optimization.
24 108 0.105659652993 Henry Cohn, 2026, needs more optimization.
24 118 0.111099565428 Henry Cohn, 2025, needs more optimization.
24 119 0.111113332243 Henry Cohn, 2026, needs more optimization.
24 121 0.111113986191 Henry Cohn, 2026, needs more optimization.
24 122 0.112368306160 Henry Cohn, 2026, needs more optimization.
24 123 0.116180792187 Henry Cohn, 2026, needs more optimization.
24 124 0.117906183525 Henry Cohn, 2026, needs more optimization.
24 125 0.122807017544 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
57⁢x−7
24 130 0.131782945737 Orthogonal union of 126 points in 22 dimensions and 4 points in 2 dimensions.
129⁢x−17
24 131 0.131783805577 Henry Cohn, 2026, needs more optimization.
24 132 0.131784194380 Henry Cohn, 2026, needs more optimization.
24 133 0.131787574814 Henry Cohn, 2026, needs more optimization.
24 134 0.131788311295 Henry Cohn, 2026, needs more optimization.
24 135 0.131963230338 Henry Cohn, 2026, needs more optimization.
24 136 0.132226461738 Henry Cohn, 2026, needs more optimization.
24 137 0.132941116529 Henry Cohn, 2026, needs more optimization.
24 138 0.133282125518 Henry Cohn, 2026, needs more optimization.
24 139 0.134487827079 Henry Cohn, 2026, needs more optimization.
24 140 0.134691765315 Henry Cohn, 2026, needs more optimization.
24 141 0.134907570741 Henry Cohn, 2026, needs more optimization.
24 142 0.135004179249 Henry Cohn, 2026, needs more optimization.
24 149 0.135135135136 Orthogonal union of 147 points in 23 dimensions and 2 points in 1 dimension.
37⁢x−5
24 150 0.135136897422 Henry Cohn, 2026, needs more optimization.
24 151 0.135200515118 Henry Cohn, 2026, needs more optimization.
24 152 0.135430863297 Henry Cohn, 2026, needs more optimization.
24 153 0.136308737406 Henry Cohn, 2026, needs more optimization.
24 154 0.139508902389 Henry Cohn, 2026, needs more optimization.
24 155 0.141727813582 Henry Cohn, 2026, needs more optimization.
24 167 0.142857140433 Henry Cohn, 2026, needs more optimization.
24 172 0.142857140440 Henry Cohn, 2026, needs more optimization.
24 174 0.142857172719 Henry Cohn, 2026, needs more optimization.
24 175 0.143721324492 Henry Cohn, 2026, needs more optimization.
24 176 0.146804013128 Henry Cohn, 2026, needs more optimization.
24 177 0.148600869869 Henry Cohn, 2026, needs more optimization.
24 178 0.150417071755 Henry Cohn, 2026, needs more optimization.
24 179 0.152871076185 Henry Cohn, 2026, needs more optimization.
24 180 0.153055874692 Henry Cohn, 2026, needs more optimization.
24 181 0.154612026824 Henry Cohn, 2026, needs more optimization.
24 182 0.155289547614 Henry Cohn, 2026, needs more optimization.
24 183 0.156525741986 Henry Cohn, 2026, needs more optimization.
24 184 0.157676003852 Henry Cohn, 2026, needs more optimization.
24 185 0.157846807820 Henry Cohn, 2026, needs more optimization.
24 186 0.158234583211 Henry Cohn, 2026, needs more optimization.
24 187 0.158751812231 Henry Cohn, 2026, needs more optimization.
24 188 0.159422102664 Henry Cohn, 2026, needs more optimization.
24 189 0.160216244002 Henry Cohn, 2026, needs more optimization.
24 190 0.160784012927 Henry Cohn, 2026, needs more optimization.
24 191 0.161760946478 Henry Cohn, 2026, needs more optimization.
24 204 0.161904761905 Code with 202 points in 23 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
105⁢x−17
24 205 0.161904762057 Orthogonal union of 201 points in 22 dimensions and 4 points in 2 dimensions.
24 212 0.161905140019 Henry Cohn, 2026, needs more optimization.
24 213 0.161972647520 Henry Cohn, 2026, needs more optimization.
24 214 0.162353490528 Henry Cohn, 2026, needs more optimization.
24 215 0.163435169251 Henry Cohn, 2026, needs more optimization.
24 216 0.164326630902 Henry Cohn, 2026, needs more optimization.
24 217 0.165193297271 Henry Cohn, 2026, needs more optimization.
24 218 0.165436326146 Henry Cohn, 2026, needs more optimization.
24 219 0.165897891113 Henry Cohn, 2026, needs more optimization.
24 220 0.166284576697 Henry Cohn, 2026, needs more optimization.
24 221 0.166376811434 Henry Cohn, 2026, needs more optimization.
24 222 0.166579076986 Henry Cohn, 2026, needs more optimization.
24 223 0.166607863008 Henry Cohn, 2026, needs more optimization.
24 224 0.166633668265 Henry Cohn, 2026, needs more optimization.
24 279 0.166666666667 Code with 277 points in 23 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
6⁢x−1
24 280 0.166725131947 Henry Cohn, 2026, needs more optimization.
24 281 0.166725569662 Henry Cohn, 2026, needs more optimization.
24 297 0.181818181819 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11⁢x−2
24 330 0.193548387097 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
31⁢x−6
24 554 0.2 Code with 552 points in 23 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−1
24 561 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 7 points in 3 dimensions.
21⁢x−5
24 564 0.238324345033 Henry Cohn, 2026, needs more optimization.
24 568 0.239006334996 Henry Cohn, 2026, needs more optimization.
24 572 0.240565555318 Henry Cohn, 2026, needs more optimization.
24 574 0.243350935121 Orthogonal union of 572 points in 23 dimensions and 2 points in 1 dimension.
24 580 0.249320155828 Henry Cohn, 2026, needs more optimization.
24 588 0.249628583856 Henry Cohn, 2026, needs more optimization.
24 596 0.249766220796 Henry Cohn, 2026, needs more optimization.
24 600 0.249965036328 Henry Cohn, 2026, needs more optimization.
24 614 0.249999999973 Henry Cohn, 2026, needs more optimization.
24 895 0.25 Orthogonal union of 891 points in 22 dimensions and 4 points in 2 dimensions.
4⁢x−1
24 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
24 196560* 0.5 J. Leech, Notes on sphere packings, Canadian J. Math. 19 (1967), 251–267, doi:10.4153/CJM-1967-017-0; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421; A. M. Odlyzko and N. J. A. Sloane, New bounds on the number of unit spheres that can touch a unit sphere in n dimensions, J. Combin. Theory Ser. A 26 (1979), 210–214, doi:10.1016/0097-3165(79)90074-8.
2⁢x−1
25 51 0.031729360276 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
13225⁢x3−625⁢x2−25⁢x+1
25 52 0.037068271283 Henry Cohn, 2025.
25 53 0.045305381447 Henry Cohn, 2025, needs more optimization.
25 54 0.045671054769 Henry Cohn, 2025.
25 55 0.046279562119 Henry Cohn, 2025.
25 56 0.046433703861 Henry Cohn, 2025, needs more optimization.
25 57 0.046863894921 Henry Cohn, 2025.
25 58 0.046863920964 Henry Cohn, 2025.
25 59 0.051394584232 Henry Cohn, 2024.
25 60 0.052987237166 Henry Cohn, 2026, needs more optimization.
25 61 0.056074458886 Henry Cohn, 2026, needs more optimization.
25 62 0.060614048413 Ilmari Vahteristo, 2026.
25 63 0.062393204143 Henry Cohn, 2026, needs more optimization.
25 64 0.064224592914 Henry Cohn, 2026, needs more optimization.
25 65 0.065096075979 Henry Cohn, 2026, needs more optimization.
25 66 0.065382268725 Henry Cohn, 2024, needs more optimization.
25 67 0.066213051890 Henry Cohn, 2026, needs more optimization.
25 68 0.066469740511 Henry Cohn, 2026, needs more optimization.
25 69 0.068628304625 Henry Cohn, 2026, needs more optimization.
25 70 0.071056156548 Henry Cohn, 2026, needs more optimization.
25 71 0.071969269199 Henry Cohn, 2026, needs more optimization.
25 72 0.075429150203 Henry Cohn, 2026, needs more optimization.
25 73 0.076552530727 Henry Cohn, 2026, needs more optimization.
25 74 0.076880068060 Henry Cohn, 2026, needs more optimization.
25 75 0.076924227688 Henry Cohn, 2026, needs more optimization.
25 76 0.076924428273 Henry Cohn, 2026, needs more optimization.
25 77 0.077472999445 Henry Cohn, 2026, needs more optimization.
25 78 0.077934807621 Henry Cohn, 2026, needs more optimization.
25 79 0.078553722337 Henry Cohn, 2026, needs more optimization.
25 80 0.080894453745 Henry Cohn, 2026, needs more optimization.
25 81 0.082238876256 Henry Cohn, 2026, needs more optimization.
25 82 0.082624250502 Henry Cohn, 2026, needs more optimization.
25 83 0.083098184781 Henry Cohn, 2026, needs more optimization.
25 84 0.083164252272 Henry Cohn, 2026, needs more optimization.
25 85 0.083277480936 Henry Cohn, 2025, needs more optimization.
25 86 0.083315721320 Henry Cohn, 2026, needs more optimization.
25 87 0.083324459220 Henry Cohn, 2026, needs more optimization.
25 88 0.083332360463 Henry Cohn, 2026, needs more optimization.
25 89 0.085175115266 Henry Cohn, 2026, needs more optimization.
25 90 0.087188062981 Henry Cohn, 2026, needs more optimization.
25 91 0.088575939960 Henry Cohn, 2026, needs more optimization.
25 92 0.089102359070 Henry Cohn, 2026, needs more optimization.
25 93 0.089851970069 Henry Cohn, 2026, needs more optimization.
25 94 0.090337394819 Henry Cohn, 2026, needs more optimization.
25 95 0.090476177284 Henry Cohn, 2026, needs more optimization.
25 96 0.090654514283 Henry Cohn, 2026, needs more optimization.
25 97 0.090861831328 Henry Cohn, 2026, needs more optimization.
25 98 0.090884763855 Henry Cohn, 2026, needs more optimization.
25 99 0.090903638972 Henry Cohn, 2026, needs more optimization.
25 106 0.090909090666 Orthogonal union of 104 points in 24 dimensions and 2 points in 1 dimension.
25 107 0.090913272191 Henry Cohn, 2026, needs more optimization.
25 108 0.093005776844 Henry Cohn, 2026, needs more optimization.
25 109 0.095561053839 Henry Cohn, 2026, needs more optimization.
25 110 0.100477491701 Henry Cohn, 2026, needs more optimization.
25 111 0.102647690180 Henry Cohn, 2026, needs more optimization.
25 112 0.105927444011 Henry Cohn, 2026, needs more optimization.
25 114 0.110979460333 Henry Cohn, 2026, needs more optimization.
25 115 0.111035532242 Henry Cohn, 2026, needs more optimization.
25 116 0.111066894552 Henry Cohn, 2026, needs more optimization.
25 119 0.111091111988 Henry Cohn, 2026, needs more optimization.
25 120 0.111099565428 Orthogonal union of 118 points in 24 dimensions and 2 points in 1 dimension.
25 123 0.111109715013 Henry Cohn, 2026, needs more optimization.
25 124 0.111110673751 Henry Cohn, 2026, needs more optimization.
25 125 0.111112955319 Henry Cohn, 2026, needs more optimization.
25 126 0.111209584994 Henry Cohn, 2026, needs more optimization.
25 127 0.114417209624 Henry Cohn, 2026, needs more optimization.
25 128 0.116274255928 Henry Cohn, 2026, needs more optimization.
25 129 0.118373234735 Henry Cohn, 2026, needs more optimization.
25 130 0.120036186929 Henry Cohn, 2026, needs more optimization.
25 131 0.122027936770 Henry Cohn, 2026, needs more optimization.
25 132 0.123583659785 Henry Cohn, 2026, needs more optimization.
25 133 0.125091451058 Henry Cohn, 2026, needs more optimization.
25 134 0.126246822279 Henry Cohn, 2026, needs more optimization.
25 135 0.128192665814 Henry Cohn, 2026, needs more optimization.
25 136 0.129733344705 Henry Cohn, 2026, needs more optimization.
25 137 0.131718880118 Henry Cohn, 2026, needs more optimization.
25 138 0.131763228461 Henry Cohn, 2026, needs more optimization.
25 139 0.131778135429 Henry Cohn, 2026, needs more optimization.
25 140 0.131785394229 Henry Cohn, 2026, needs more optimization.
25 141 0.131919356278 Henry Cohn, 2026, needs more optimization.
25 156 0.133333333334 Henry Cohn, 2023. In Ericson and Zinoviev's notation, this code is the union of a code constructed by CW2 from C : (26,6,8,130) and -S25 by CW2.
15⁢x−2
25 157 0.135174273058 Henry Cohn, 2026, needs more optimization.
25 158 0.137173809024 Henry Cohn, 2026, needs more optimization.
25 159 0.138900346840 Henry Cohn, 2026, needs more optimization.
25 160 0.140564274886 Henry Cohn, 2026, needs more optimization.
25 161 0.141385165368 Henry Cohn, 2026, needs more optimization.
25 169 0.142857140433 Orthogonal union of 167 points in 24 dimensions and 2 points in 1 dimension.
25 174 0.142857140440 Orthogonal union of 172 points in 24 dimensions and 2 points in 1 dimension.
25 176 0.142857172719 Orthogonal union of 174 points in 24 dimensions and 2 points in 1 dimension.
25 177 0.142871291590 Henry Cohn, 2026, needs more optimization.
25 178 0.142905507749 Henry Cohn, 2026, needs more optimization.
25 179 0.143288197044 Henry Cohn, 2026, needs more optimization.
25 180 0.143308401237 Henry Cohn, 2026, needs more optimization.
25 182 0.144754392163 Henry Cohn, 2026, needs more optimization.
25 183 0.146087594665 Henry Cohn, 2026, needs more optimization.
25 184 0.147875564169 Henry Cohn, 2026, needs more optimization.
25 185 0.150256923482 Henry Cohn, 2026, needs more optimization.
25 186 0.150962876902 Henry Cohn, 2026, needs more optimization.
25 187 0.152056095966 Henry Cohn, 2026, needs more optimization.
25 188 0.153413695528 Henry Cohn, 2026, needs more optimization.
25 189 0.154915978779 Henry Cohn, 2026, needs more optimization.
25 190 0.155485632908 Henry Cohn, 2026, needs more optimization.
25 191 0.156235559679 Henry Cohn, 2026, needs more optimization.
25 192 0.157073618729 Henry Cohn, 2026, needs more optimization.
25 193 0.157676781469 Henry Cohn, 2026, needs more optimization.
25 194 0.158291928149 Henry Cohn, 2026, needs more optimization.
25 195 0.159212231246 Henry Cohn, 2026, needs more optimization.
25 196 0.159247170475 Henry Cohn, 2026, needs more optimization.
25 198 0.159497198872 Henry Cohn, 2026, needs more optimization.
25 199 0.160422841196 Henry Cohn, 2026, needs more optimization.
25 200 0.160778704859 Henry Cohn, 2026, needs more optimization.
25 201 0.161459246081 Henry Cohn, 2026, needs more optimization.
25 205 0.161888084131 Henry Cohn, 2026, needs more optimization.
25 206 0.161890055666 Henry Cohn, 2025, needs more optimization.
25 208 0.161897664760 Henry Cohn, 2026, needs more optimization.
25 209 0.161900141318 Henry Cohn, 2026, needs more optimization.
25 211 0.161903212778 Henry Cohn, 2026, needs more optimization.
25 212 0.161903902009 Henry Cohn, 2026, needs more optimization.
25 214 0.161905140019 Orthogonal union of 212 points in 24 dimensions and 2 points in 1 dimension.
25 215 0.161906957650 Henry Cohn, 2026, needs more optimization.
25 216 0.161908025900 Henry Cohn, 2026, needs more optimization.
25 218 0.161921395676 Henry Cohn, 2026, needs more optimization.
25 219 0.161955693228 Henry Cohn, 2026, needs more optimization.
25 220 0.162247049168 Henry Cohn, 2026, needs more optimization.
25 221 0.164711057096 Henry Cohn, 2026, needs more optimization.
25 224 0.164712759150 Henry Cohn, 2026, needs more optimization.
25 225 0.166607863008 Orthogonal union of 223 points in 24 dimensions and 2 points in 1 dimension.
25 226 0.166633668265 Orthogonal union of 224 points in 24 dimensions and 2 points in 1 dimension.
25 281 0.166666666667 Orthogonal union of 275 points in 22 dimensions and 6 points in 3 dimensions.
6⁢x−1
25 283 0.166712841552 Henry Cohn, 2026, needs more optimization.
25 284 0.179533531202 Henry Cohn, 2026, needs more optimization.
25 287 0.179536387249 Henry Cohn, 2026, needs more optimization.
25 288 0.179746398971 Henry Cohn, 2026, needs more optimization.
25 299 0.181818181819 Orthogonal union of 297 points in 24 dimensions and 2 points in 1 dimension.
11⁢x−2
25 332 0.193548387097 Orthogonal union of 330 points in 24 dimensions and 2 points in 1 dimension.
31⁢x−6
25 556 0.2 Orthogonal union of 552 points in 23 dimensions and 4 points in 2 dimensions.
5⁢x−1
25 566 0.238095238096 Henry Cohn, 2025.
21⁢x−5
25 567 0.238140742993 Henry Cohn, 2025, needs more optimization.
25 568 0.238222097670 Henry Cohn, 2026, needs more optimization.
25 572 0.238225652680 Henry Cohn, 2026, needs more optimization.
25 576 0.238455704035 Henry Cohn, 2026, needs more optimization.
25 580 0.239534136427 Henry Cohn, 2026, needs more optimization.
25 588 0.241805634200 Henry Cohn, 2026, needs more optimization.
25 596 0.244843693358 Henry Cohn, 2026, needs more optimization.
25 600 0.247273777413 Henry Cohn, 2026, needs more optimization.
25 604 0.247283994767 Henry Cohn, 2026, needs more optimization.
25 612 0.248651724434 Henry Cohn, 2026, needs more optimization.
25 616 0.249338895785 Henry Cohn, 2026, needs more optimization.
25 620 0.249373494425 Henry Cohn, 2026, needs more optimization.
25 628 0.249672626512 Henry Cohn, 2026, needs more optimization.
25 632 0.249856248211 Henry Cohn, 2026, needs more optimization.
25 636 0.249889236005 Henry Cohn, 2026, needs more optimization.
25 640 0.249975942437 Henry Cohn, 2026, needs more optimization.
25 642 0.249995385048 Henry Cohn, 2026, needs more optimization.
25 900 0.25 Henry Cohn, 2025.
4⁢x−1
25 901 0.250172215665 Henry Cohn, 2025, needs more optimization.
25 902 0.250173848877 Henry Cohn, 2026, needs more optimization.
25 903 0.250187558714 Henry Cohn, 2025, needs more optimization.
25 904 0.250190030344 Henry Cohn, 2026, needs more optimization.
25 905 0.250195554497 Henry Cohn, 2025, needs more optimization.
25 906 0.250276133393 Henry Cohn, 2026, needs more optimization.
25 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
26 53 0.030620650808 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
14976⁢x3−676⁢x2−26⁢x+1
26 54 0.035747894971 Henry Cohn, 2026, needs more optimization.
26 55 0.044558069283 Henry Cohn, 2026, needs more optimization.
26 56 0.044663560912 Henry Cohn, 2026, needs more optimization.
26 57 0.045162601400 Henry Cohn, 2026, needs more optimization.
26 58 0.045550434603 Henry Cohn, 2024.
26 59 0.046163974402 Henry Cohn, 2025.
26 60 0.046456376998 Henry Cohn, 2026, needs more optimization.
26 61 0.049243792051 Henry Cohn, 2026, needs more optimization.
26 62 0.051910677056 Henry Cohn, 2026, needs more optimization.
26 63 0.054440031786 Henry Cohn, 2026, needs more optimization.
26 64 0.057479203623 Henry Cohn, 2026, needs more optimization.
26 65 0.060321922991 Ilmari Vahteristo, 2026.
26 66 0.062271265030 Ilmari Vahteristo, 2026.
26 67 0.063559236059 Henry Cohn, 2026, needs more optimization.
26 68 0.063600411345 Henry Cohn, 2026, needs more optimization.
26 69 0.064916629007 Henry Cohn, 2026, needs more optimization.
26 70 0.065400202147 Henry Cohn, 2026, needs more optimization.
26 71 0.067315893910 Henry Cohn, 2026, needs more optimization.
26 72 0.068297564169 Henry Cohn, 2026, needs more optimization.
26 73 0.070999329472 Henry Cohn, 2026, needs more optimization.
26 74 0.073191112187 Henry Cohn, 2026, needs more optimization.
26 75 0.074411709885 Henry Cohn, 2026, needs more optimization.
26 76 0.075418506387 Henry Cohn, 2026, needs more optimization.
26 77 0.076589754502 Henry Cohn, 2026, needs more optimization.
26 78 0.076864990301 Henry Cohn, 2026, needs more optimization.
26 79 0.076920089242 Henry Cohn, 2026, needs more optimization.
26 80 0.076967648257 Henry Cohn, 2026, needs more optimization.
26 81 0.077577286856 Henry Cohn, 2026, needs more optimization.
26 82 0.077924828167 Henry Cohn, 2026, needs more optimization.
26 83 0.079100881430 Henry Cohn, 2026, needs more optimization.
26 84 0.079410382251 Henry Cohn, 2026, needs more optimization.
26 85 0.081913532502 Henry Cohn, 2026, needs more optimization.
26 86 0.082680160885 Henry Cohn, 2026, needs more optimization.
26 87 0.082856208664 Henry Cohn, 2026, needs more optimization.
26 88 0.082972222894 Henry Cohn, 2026, needs more optimization.
26 89 0.083272866986 Henry Cohn, 2026, needs more optimization.
26 90 0.083304500874 Henry Cohn, 2026, needs more optimization.
26 91 0.083321524096 Henry Cohn, 2026, needs more optimization.
26 92 0.084415236972 Henry Cohn, 2026, needs more optimization.
26 93 0.085534564383 Henry Cohn, 2026, needs more optimization.
26 94 0.086904725611 Henry Cohn, 2026, needs more optimization.
26 95 0.088409155005 Henry Cohn, 2026, needs more optimization.
26 96 0.088785257959 Henry Cohn, 2026, needs more optimization.
26 97 0.089476909408 Henry Cohn, 2026, needs more optimization.
26 98 0.089870154125 Henry Cohn, 2026, needs more optimization.
26 99 0.090269132945 Henry Cohn, 2026, needs more optimization.
26 100 0.090364089552 Henry Cohn, 2026, needs more optimization.
26 101 0.090572460120 Henry Cohn, 2026, needs more optimization.
26 102 0.090760757619 Henry Cohn, 2026, needs more optimization.
26 103 0.090857578317 Henry Cohn, 2026, needs more optimization.
26 104 0.090890636960 Henry Cohn, 2026, needs more optimization.
26 105 0.090905683490 Henry Cohn, 2026, needs more optimization.
26 108 0.090909090666 Orthogonal union of 104 points in 24 dimensions and 4 points in 2 dimensions.
26 109 0.090911118785 Henry Cohn, 2026, needs more optimization.
26 110 0.090912497041 Henry Cohn, 2026, needs more optimization.
26 111 0.091921189353 Henry Cohn, 2026, needs more optimization.
26 112 0.094599007120 Henry Cohn, 2026, needs more optimization.
26 113 0.097432440644 Henry Cohn, 2026, needs more optimization.
26 114 0.100904545962 Henry Cohn, 2026, needs more optimization.
26 119 0.103125332235 Henry Cohn, 2026.
191⁢x2−10⁢x−1
26 120 0.103389121229 Henry Cohn, 2026, needs more optimization.
26 121 0.104307918182 Henry Cohn, 2026, needs more optimization.
26 122 0.105681671502 Henry Cohn, 2026, needs more optimization.
26 123 0.106265325565 Henry Cohn, 2026, needs more optimization.
26 124 0.107210105932 Henry Cohn, 2026, needs more optimization.
26 125 0.108133623541 Henry Cohn, 2026, needs more optimization.
26 126 0.108579423630 Henry Cohn, 2026, needs more optimization.
26 127 0.109241324492 Henry Cohn, 2026, needs more optimization.
26 128 0.111085523762 Henry Cohn, 2026, needs more optimization.
26 129 0.111107331306 Henry Cohn, 2026, needs more optimization.
26 130 0.111111559811 Henry Cohn, 2026, needs more optimization.
26 131 0.111127749049 Henry Cohn, 2026, needs more optimization.
26 132 0.114340043771 Henry Cohn, 2026, needs more optimization.
26 133 0.115162675930 Henry Cohn, 2026, needs more optimization.
26 134 0.116479965617 Henry Cohn, 2026, needs more optimization.
26 135 0.119557262077 Henry Cohn, 2026, needs more optimization.
26 136 0.121071198277 Henry Cohn, 2026, needs more optimization.
26 137 0.121421384805 Henry Cohn, 2026, needs more optimization.
26 138 0.122301886438 Henry Cohn, 2026, needs more optimization.
26 139 0.124679413752 Henry Cohn, 2026, needs more optimization.
26 140 0.127204785273 Henry Cohn, 2026, needs more optimization.
26 141 0.129700006248 Henry Cohn, 2026, needs more optimization.
26 143 0.131473144128 Henry Cohn, 2026, needs more optimization.
26 144 0.131692066683 Henry Cohn, 2026, needs more optimization.
26 145 0.131732748026 Henry Cohn, 2026, needs more optimization.
26 146 0.131788609213 Henry Cohn, 2026, needs more optimization.
26 147 0.131911831435 Henry Cohn, 2026, needs more optimization.
26 148 0.132502045423 Henry Cohn, 2026, needs more optimization.
26 158 0.133333333334 Orthogonal union of 156 points in 25 dimensions and 2 points in 1 dimension.
15⁢x−2
26 159 0.133341767968 Henry Cohn, 2026, needs more optimization.
26 160 0.134598515128 Henry Cohn, 2026, needs more optimization.
26 161 0.135140901809 Henry Cohn, 2026, needs more optimization.
26 162 0.135384609263 Henry Cohn, 2026, needs more optimization.
26 163 0.136053494519 Henry Cohn, 2026, needs more optimization.
26 164 0.136787994085 Henry Cohn, 2026, needs more optimization.
26 165 0.138337750989 Henry Cohn, 2026, needs more optimization.
26 166 0.138941425009 Henry Cohn, 2026, needs more optimization.
26 167 0.140493277028 Henry Cohn, 2026, needs more optimization.
26 168 0.141052193033 Henry Cohn, 2026, needs more optimization.
26 169 0.142720244578 Henry Cohn, 2026, needs more optimization.
26 170 0.142752962155 Henry Cohn, 2026, needs more optimization.
26 172 0.142811088702 Henry Cohn, 2026, needs more optimization.
26 173 0.142815649215 Henry Cohn, 2026, needs more optimization.
26 176 0.142827056151 Henry Cohn, 2026, needs more optimization.
26 178 0.142829684486 Henry Cohn, 2026, needs more optimization.
26 179 0.142836341515 Henry Cohn, 2026, needs more optimization.
26 180 0.142838771815 Henry Cohn, 2026, needs more optimization.
26 181 0.142846067132 Henry Cohn, 2026, needs more optimization.
26 182 0.142854438901 Henry Cohn, 2026, needs more optimization.
26 183 0.142862036052 Henry Cohn, 2026, needs more optimization.
26 184 0.142882056392 Henry Cohn, 2026, needs more optimization.
26 185 0.142933680729 Henry Cohn, 2026, needs more optimization.
26 186 0.143306332668 Henry Cohn, 2026, needs more optimization.
26 187 0.144119674839 Henry Cohn, 2026, needs more optimization.
26 188 0.145491106769 Henry Cohn, 2026, needs more optimization.
26 189 0.146762402220 Henry Cohn, 2026, needs more optimization.
26 190 0.148056964477 Henry Cohn, 2026, needs more optimization.
26 191 0.149212065856 Henry Cohn, 2026, needs more optimization.
26 192 0.150074064370 Henry Cohn, 2026, needs more optimization.
26 193 0.150195612350 Henry Cohn, 2026, needs more optimization.
26 194 0.151702521411 Henry Cohn, 2026, needs more optimization.
26 195 0.152648135006 Henry Cohn, 2026, needs more optimization.
26 196 0.153259064375 Henry Cohn, 2026, needs more optimization.
26 197 0.153302819825 Henry Cohn, 2026, needs more optimization.
26 198 0.154444484855 Henry Cohn, 2026, needs more optimization.
26 199 0.155451057855 Henry Cohn, 2026, needs more optimization.
26 200 0.155770576513 Henry Cohn, 2026, needs more optimization.
26 201 0.156527875733 Henry Cohn, 2026, needs more optimization.
26 202 0.157036995118 Henry Cohn, 2026, needs more optimization.
26 203 0.157294146581 Henry Cohn, 2026, needs more optimization.
26 204 0.157962916314 Henry Cohn, 2026, needs more optimization.
26 205 0.158359457492 Henry Cohn, 2026, needs more optimization.
26 206 0.159026809495 Henry Cohn, 2026, needs more optimization.
26 207 0.159346677322 Henry Cohn, 2026, needs more optimization.
26 208 0.159687686389 Henry Cohn, 2026, needs more optimization.
26 209 0.159928867955 Henry Cohn, 2026, needs more optimization.
26 210 0.160389616837 Henry Cohn, 2026, needs more optimization.
26 211 0.160833415503 Henry Cohn, 2026, needs more optimization.
26 213 0.161234634043 Henry Cohn, 2026, needs more optimization.
26 214 0.161593359953 Henry Cohn, 2026, needs more optimization.
26 217 0.161860126522 Henry Cohn, 2026, needs more optimization.
26 218 0.161868865949 Henry Cohn, 2026, needs more optimization.
26 219 0.161875456515 Henry Cohn, 2026, needs more optimization.
26 221 0.161889890677 Henry Cohn, 2026, needs more optimization.
26 225 0.161911531138 Henry Cohn, 2026, needs more optimization.
26 227 0.161983210773 Henry Cohn, 2026, needs more optimization.
26 228 0.162054821023 Henry Cohn, 2026, needs more optimization.
26 229 0.162405138372 Henry Cohn, 2026, needs more optimization.
26 230 0.162588295291 Henry Cohn, 2026, needs more optimization.
26 231 0.162694975431 Henry Cohn, 2026, needs more optimization.
26 232 0.164613568793 Henry Cohn, 2026, needs more optimization.
26 234 0.164915453186 Henry Cohn, 2026, needs more optimization.
26 235 0.165109450766 Henry Cohn, 2026, needs more optimization.
26 236 0.166472443455 Henry Cohn, 2026, needs more optimization.
26 285 0.166666666667 Orthogonal union of 275 points in 22 dimensions and 10 points in 4 dimensions.
6⁢x−1
26 286 0.179533531202 Orthogonal union of 284 points in 25 dimensions and 2 points in 1 dimension.
26 289 0.179536387249 Orthogonal union of 287 points in 25 dimensions and 2 points in 1 dimension.
26 291 0.179540728357 Henry Cohn, 2026, needs more optimization.
26 292 0.179541108819 Henry Cohn, 2026, needs more optimization.
26 296 0.179551049602 Henry Cohn, 2026, needs more optimization.
26 297 0.179672295545 Henry Cohn, 2026, needs more optimization.
26 298 0.180327752656 Henry Cohn, 2026, needs more optimization.
26 301 0.181818181819 Orthogonal union of 297 points in 24 dimensions and 4 points in 2 dimensions.
11⁢x−2
26 334 0.193548387097 Orthogonal union of 330 points in 24 dimensions and 4 points in 2 dimensions.
31⁢x−6
26 558 0.2 Orthogonal union of 552 points in 23 dimensions and 6 points in 3 dimensions.
5⁢x−1
26 559 0.200074016035 Henry Cohn, 2026, needs more optimization.
26 560 0.200082923136 Henry Cohn, 2025, needs more optimization.
26 562 0.200092912683 Henry Cohn, 2026, needs more optimization.
26 563 0.200101611377 Henry Cohn, 2026, needs more optimization.
26 570 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 16 points in 5 dimensions.
21⁢x−5
26 572 0.238172425447 Henry Cohn, 2026, needs more optimization.
26 576 0.238219624605 Henry Cohn, 2026, needs more optimization.
26 580 0.238307863858 Henry Cohn, 2026, needs more optimization.
26 588 0.238593885182 Henry Cohn, 2026, needs more optimization.
26 596 0.239608145954 Henry Cohn, 2026, needs more optimization.
26 604 0.242894710613 Henry Cohn, 2026, needs more optimization.
26 612 0.245725454066 Henry Cohn, 2026, needs more optimization.
26 620 0.247512109662 Henry Cohn, 2026, needs more optimization.
26 628 0.248468221990 Henry Cohn, 2026, needs more optimization.
26 632 0.249084908179 Henry Cohn, 2026, needs more optimization.
26 635 0.249218339467 Henry Cohn, 2026, needs more optimization.
26 636 0.249218339690 Henry Cohn, 2026, needs more optimization.
26 644 0.249645265443 Henry Cohn, 2026, needs more optimization.
26 652 0.249824023123 Henry Cohn, 2026, needs more optimization.
26 660 0.249913277894 Henry Cohn, 2026, needs more optimization.
26 664 0.249960889164 Henry Cohn, 2026, needs more optimization.
26 666 0.249992105150 Henry Cohn, 2026, needs more optimization.
26 903 0.25 Orthogonal union of 891 points in 22 dimensions and 12 points in 4 dimensions.
4⁢x−1
26 906 0.250126950667 Henry Cohn, 2026, needs more optimization.
26 907 0.250132202205 Henry Cohn, 2025, needs more optimization.
26 908 0.250172640654 Henry Cohn, 2026, needs more optimization.
26 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
27 55 0.029589200879 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
16875⁢x3−729⁢x2−27⁢x+1
27 56 0.034511432831 Henry Cohn, 2024.
27 57 0.043679995742 Henry Cohn, 2024.
27 58 0.044384904811 Henry Cohn, 2026, needs more optimization.
27 59 0.044780194273 Henry Cohn, 2026, needs more optimization.
27 60 0.045477973897 Henry Cohn, 2024, needs more optimization.
27 61 0.045484387668 Henry Cohn, 2024, needs more optimization.
27 62 0.046198040189 Henry Cohn, 2025.
27 63 0.047991049633 Henry Cohn, 2026, needs more optimization.
27 64 0.050774548483 Henry Cohn, 2026, needs more optimization.
27 65 0.054278580194 Ilmari Vahteristo, 2026.
27 66 0.056579900424 Ilmari Vahteristo, 2026.
27 67 0.058508943115 Ilmari Vahteristo, 2026.
27 68 0.060168732746 Henry Cohn, 2026, needs more optimization.
27 69 0.061863738855 Ilmari Vahteristo, 2026.
27 70 0.062922671894 Henry Cohn, 2026, needs more optimization.
27 71 0.064107549690 Henry Cohn, 2026, needs more optimization.
27 72 0.064938703566 Henry Cohn, 2026, needs more optimization.
27 73 0.065805542879 Henry Cohn, 2026, needs more optimization.
27 74 0.066383272572 Henry Cohn, 2026, needs more optimization.
27 75 0.068128633261 Henry Cohn, 2026, needs more optimization.
27 76 0.070113017465 Henry Cohn, 2026, needs more optimization.
27 77 0.072327221285 Henry Cohn, 2026, needs more optimization.
27 78 0.074625002823 Henry Cohn, 2026, needs more optimization.
27 79 0.075331327438 Henry Cohn, 2026, needs more optimization.
27 80 0.076122276909 Henry Cohn, 2026, needs more optimization.
27 81 0.076640303489 Henry Cohn, 2026, needs more optimization.
27 82 0.076894452895 Henry Cohn, 2026, needs more optimization.
27 83 0.076959451300 Henry Cohn, 2026, needs more optimization.
27 84 0.077059848801 Henry Cohn, 2026, needs more optimization.
27 85 0.077375337867 Henry Cohn, 2026, needs more optimization.
27 86 0.077736768150 Henry Cohn, 2026, needs more optimization.
27 87 0.078534957484 Henry Cohn, 2026, needs more optimization.
27 88 0.078632181819 Henry Cohn, 2026, needs more optimization.
27 89 0.080684193393 Henry Cohn, 2026, needs more optimization.
27 93 0.080684279095 Henry Cohn, 2026, needs more optimization.
27 95 0.080685804300 Henry Cohn, 2026, needs more optimization.
27 96 0.080686096040 Henry Cohn, 2026, needs more optimization.
27 97 0.080727820996 Henry Cohn, 2026, needs more optimization.
27 98 0.081848844477 Henry Cohn, 2026, needs more optimization.
27 99 0.087578953303 Henry Cohn, 2026, needs more optimization.
27 100 0.088309371252 Henry Cohn, 2026, needs more optimization.
27 101 0.088922675676 Henry Cohn, 2026, needs more optimization.
27 102 0.089495202410 Henry Cohn, 2026, needs more optimization.
27 103 0.090134999465 Henry Cohn, 2026, needs more optimization.
27 104 0.090258381350 Henry Cohn, 2026, needs more optimization.
27 105 0.090552549258 Henry Cohn, 2026, needs more optimization.
27 106 0.090633494174 Henry Cohn, 2026, needs more optimization.
27 107 0.090714661919 Henry Cohn, 2026, needs more optimization.
27 108 0.090773036350 Henry Cohn, 2026, needs more optimization.
27 109 0.090814020245 Henry Cohn, 2026, needs more optimization.
27 110 0.090870650464 Henry Cohn, 2024, needs more optimization.
27 111 0.090892250095 Henry Cohn, 2026, needs more optimization.
27 112 0.090907019693 Henry Cohn, 2026, needs more optimization.
27 113 0.090909413844 Henry Cohn, 2026, needs more optimization.
27 114 0.091617243612 Henry Cohn, 2026, needs more optimization.
27 115 0.093250361511 Henry Cohn, 2026, needs more optimization.
27 116 0.095893983551 Henry Cohn, 2026, needs more optimization.
27 117 0.098876011407 Henry Cohn, 2026, needs more optimization.
27 118 0.101376692034 Henry Cohn, 2026, needs more optimization.
27 121 0.103125332235 Orthogonal union of 119 points in 26 dimensions and 2 points in 1 dimension.
191⁢x2−10⁢x−1
27 123 0.103125332798 Henry Cohn, 2026, needs more optimization.
27 125 0.103125336303 Henry Cohn, 2026, needs more optimization.
27 126 0.104878726889 Henry Cohn, 2026, needs more optimization.
27 127 0.106667465179 Henry Cohn, 2026, needs more optimization.
27 128 0.106848727573 Henry Cohn, 2026, needs more optimization.
27 129 0.107240835781 Henry Cohn, 2026, needs more optimization.
27 130 0.107692441329 Henry Cohn, 2026, needs more optimization.
27 131 0.109123186106 Henry Cohn, 2026, needs more optimization.
27 132 0.109633505861 Henry Cohn, 2026, needs more optimization.
27 133 0.110569214799 Henry Cohn, 2026, needs more optimization.
27 134 0.111032493963 Henry Cohn, 2026, needs more optimization.
27 135 0.111034840474 Henry Cohn, 2026, needs more optimization.
27 136 0.111797816791 Henry Cohn, 2026, needs more optimization.
27 137 0.113545876611 Henry Cohn, 2026, needs more optimization.
27 138 0.114548825535 Henry Cohn, 2026, needs more optimization.
27 139 0.114846806012 Henry Cohn, 2026, needs more optimization.
27 140 0.116042872472 Henry Cohn, 2026, needs more optimization.
27 141 0.116318048118 Henry Cohn, 2026, needs more optimization.
27 142 0.117570362120 Henry Cohn, 2026, needs more optimization.
27 143 0.120407933403 Henry Cohn, 2026, needs more optimization.
27 144 0.121001772639 Henry Cohn, 2026, needs more optimization.
27 145 0.123136128169 Henry Cohn, 2026, needs more optimization.
27 146 0.125388443993 Henry Cohn, 2026, needs more optimization.
27 147 0.127237443108 Henry Cohn, 2026, needs more optimization.
27 148 0.129864440947 Henry Cohn, 2026, needs more optimization.
27 149 0.131294176852 Henry Cohn, 2026, needs more optimization.
27 150 0.131489649095 Henry Cohn, 2026, needs more optimization.
27 151 0.132806808217 Henry Cohn, 2026, needs more optimization.
27 152 0.132866170261 Henry Cohn, 2026, needs more optimization.
27 153 0.132933263726 Henry Cohn, 2026, needs more optimization.
27 154 0.132988279042 Henry Cohn, 2026, needs more optimization.
27 155 0.133181600613 Henry Cohn, 2026, needs more optimization.
27 156 0.133234201816 Henry Cohn, 2026, needs more optimization.
27 157 0.133259876548 Henry Cohn, 2026, needs more optimization.
27 160 0.133281675069 Henry Cohn, 2026, needs more optimization.
27 161 0.133306800091 Henry Cohn, 2026, needs more optimization.
27 162 0.133328342255 Henry Cohn, 2026, needs more optimization.
27 163 0.133332016249 Henry Cohn, 2026, needs more optimization.
27 164 0.133500761754 Henry Cohn, 2026, needs more optimization.
27 166 0.135091594904 Henry Cohn, 2026, needs more optimization.
27 167 0.135116296886 Henry Cohn, 2026, needs more optimization.
27 168 0.135150499509 Henry Cohn, 2026, needs more optimization.
27 169 0.135342983092 Henry Cohn, 2026, needs more optimization.
27 170 0.135944002630 Henry Cohn, 2026, needs more optimization.
27 171 0.136779235982 Henry Cohn, 2026, needs more optimization.
27 172 0.137425411981 Henry Cohn, 2026, needs more optimization.
27 173 0.138959429809 Henry Cohn, 2026, needs more optimization.
27 174 0.139783459198 Henry Cohn, 2026, needs more optimization.
27 175 0.141047989264 Henry Cohn, 2026, needs more optimization.
27 176 0.142463353894 Henry Cohn, 2026, needs more optimization.
27 177 0.142493557618 Henry Cohn, 2026, needs more optimization.
27 178 0.142515678753 Henry Cohn, 2026, needs more optimization.
27 179 0.142583301323 Henry Cohn, 2026, needs more optimization.
27 180 0.142635657708 Henry Cohn, 2026, needs more optimization.
27 181 0.142676987052 Henry Cohn, 2026, needs more optimization.
27 182 0.142704140842 Henry Cohn, 2026, needs more optimization.
27 183 0.142717467068 Henry Cohn, 2026, needs more optimization.
27 185 0.142762596907 Henry Cohn, 2026, needs more optimization.
27 186 0.142777484679 Henry Cohn, 2026, needs more optimization.
27 187 0.142799806623 Henry Cohn, 2026, needs more optimization.
27 188 0.142806232499 Henry Cohn, 2026, needs more optimization.
27 189 0.142813772479 Henry Cohn, 2026, needs more optimization.
27 190 0.142829747582 Henry Cohn, 2026, needs more optimization.
27 191 0.142865564638 Henry Cohn, 2026, needs more optimization.
27 192 0.143076333978 Henry Cohn, 2026, needs more optimization.
27 193 0.143218525918 Henry Cohn, 2026, needs more optimization.
27 194 0.143951734956 Henry Cohn, 2026, needs more optimization.
27 195 0.145449132970 Henry Cohn, 2026, needs more optimization.
27 196 0.146195800191 Henry Cohn, 2026, needs more optimization.
27 197 0.146680515904 Henry Cohn, 2026, needs more optimization.
27 198 0.147574571769 Henry Cohn, 2026, needs more optimization.
27 199 0.148384094301 Henry Cohn, 2026, needs more optimization.
27 200 0.148972318596 Henry Cohn, 2026, needs more optimization.
27 201 0.150007054145 Henry Cohn, 2026, needs more optimization.
27 202 0.151535417657 Henry Cohn, 2026, needs more optimization.
27 203 0.152226230306 Henry Cohn, 2026, needs more optimization.
27 204 0.153663302273 Henry Cohn, 2026, needs more optimization.
27 205 0.154603081441 Henry Cohn, 2026, needs more optimization.
27 207 0.155173741510 Henry Cohn, 2026, needs more optimization.
27 208 0.155585074527 Henry Cohn, 2026, needs more optimization.
27 209 0.156138413052 Henry Cohn, 2026, needs more optimization.
27 210 0.156811559767 Henry Cohn, 2026, needs more optimization.
27 211 0.157234073034 Henry Cohn, 2026, needs more optimization.
27 212 0.157624499963 Henry Cohn, 2026, needs more optimization.
27 213 0.158078191663 Henry Cohn, 2026, needs more optimization.
27 214 0.158693788193 Henry Cohn, 2026, needs more optimization.
27 215 0.159238150539 Henry Cohn, 2026, needs more optimization.
27 216 0.159259997847 Henry Cohn, 2026, needs more optimization.
27 217 0.159679813669 Henry Cohn, 2026, needs more optimization.
27 218 0.160157758391 Henry Cohn, 2026, needs more optimization.
27 219 0.160536340468 Henry Cohn, 2026, needs more optimization.
27 220 0.161567357429 Henry Cohn, 2026, needs more optimization.
27 221 0.161597809935 Henry Cohn, 2026, needs more optimization.
27 222 0.161640899830 Henry Cohn, 2026, needs more optimization.
27 223 0.161716190392 Henry Cohn, 2026, needs more optimization.
27 224 0.161726521527 Henry Cohn, 2026, needs more optimization.
27 225 0.161761903308 Henry Cohn, 2026, needs more optimization.
27 226 0.161766235904 Henry Cohn, 2026, needs more optimization.
27 227 0.161771053879 Henry Cohn, 2026, needs more optimization.
27 228 0.161776510128 Henry Cohn, 2026, needs more optimization.
27 229 0.161784900622 Henry Cohn, 2026, needs more optimization.
27 230 0.161795356459 Henry Cohn, 2026, needs more optimization.
27 231 0.161858738350 Henry Cohn, 2026, needs more optimization.
27 232 0.161888218859 Henry Cohn, 2026, needs more optimization.
27 235 0.161890207420 Henry Cohn, 2026, needs more optimization.
27 237 0.161965564949 Henry Cohn, 2026, needs more optimization.
27 238 0.162440623494 Henry Cohn, 2026, needs more optimization.
27 239 0.162927835686 Henry Cohn, 2026, needs more optimization.
27 240 0.163014821790 Henry Cohn, 2026, needs more optimization.
27 241 0.163345086587 Henry Cohn, 2026, needs more optimization.
27 243 0.163448848811 Henry Cohn, 2026, needs more optimization.
27 245 0.165099354590 Henry Cohn, 2026, needs more optimization.
27 247 0.165171967135 Henry Cohn, 2026, needs more optimization.
27 248 0.165913619392 Henry Cohn, 2026, needs more optimization.
27 287 0.166666666667 Orthogonal union of 275 points in 22 dimensions and 12 points in 5 dimensions.
6⁢x−1
27 288 0.166687947349 Henry Cohn, 2026, needs more optimization.
27 289 0.166696111005 Henry Cohn, 2026, needs more optimization.
27 290 0.179492432689 Henry Cohn, 2026, needs more optimization.
27 291 0.179492839372 Henry Cohn, 2026, needs more optimization.
27 292 0.179493118776 Henry Cohn, 2026, needs more optimization.
27 293 0.179493566291 Henry Cohn, 2026, needs more optimization.
27 294 0.179493965203 Henry Cohn, 2026, needs more optimization.
27 295 0.179494496941 Henry Cohn, 2026, needs more optimization.
27 296 0.179494996359 Henry Cohn, 2026, needs more optimization.
27 297 0.179495688918 Henry Cohn, 2026, needs more optimization.
27 298 0.179496613103 Henry Cohn, 2026, needs more optimization.
27 299 0.179498235412 Henry Cohn, 2026, needs more optimization.
27 300 0.179500637410 Henry Cohn, 2026, needs more optimization.
27 301 0.179572440091 Henry Cohn, 2026, needs more optimization.
27 303 0.181818181819 Orthogonal union of 297 points in 24 dimensions and 6 points in 3 dimensions.
11⁢x−2
27 336 0.193548387097 Orthogonal union of 330 points in 24 dimensions and 6 points in 3 dimensions.
31⁢x−6
27 340 0.196416196148 Henry Cohn, 2026, needs more optimization.
27 562 0.2 Orthogonal union of 552 points in 23 dimensions and 10 points in 4 dimensions.
5⁢x−1
27 563 0.200069910253 Henry Cohn, 2026, needs more optimization.
27 564 0.200071739851 Henry Cohn, 2025, needs more optimization.
27 566 0.200076155705 Henry Cohn, 2025, needs more optimization.
27 568 0.200135182099 Henry Cohn, 2026, needs more optimization.
27 574 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 20 points in 6 dimensions.
21⁢x−5
27 576 0.238109925296 Henry Cohn, 2026, needs more optimization.
27 577 0.238137087627 Henry Cohn, 2026, needs more optimization.
27 580 0.238142233407 Henry Cohn, 2026, needs more optimization.
27 588 0.238161083887 Henry Cohn, 2026, needs more optimization.
27 596 0.238207206832 Henry Cohn, 2026, needs more optimization.
27 604 0.238399890402 Henry Cohn, 2026, needs more optimization.
27 612 0.239166035658 Henry Cohn, 2026, needs more optimization.
27 620 0.241495642847 Henry Cohn, 2026, needs more optimization.
27 628 0.244293223902 Henry Cohn, 2026, needs more optimization.
27 636 0.246018298720 Henry Cohn, 2026, needs more optimization.
27 644 0.247363798966 Henry Cohn, 2026, needs more optimization.
27 652 0.248274699172 Henry Cohn, 2026, needs more optimization.
27 660 0.248937425811 Henry Cohn, 2026, needs more optimization.
27 668 0.249461567860 Henry Cohn, 2026, needs more optimization.
27 676 0.249707754126 Henry Cohn, 2026, needs more optimization.
27 686 0.249788297044 Henry Cohn, 2026, needs more optimization.
27 690 0.249891443396 Henry Cohn, 2026, needs more optimization.
27 692 0.249949554902 Henry Cohn, 2026, needs more optimization.
27 907 0.25 Orthogonal union of 891 points in 22 dimensions and 16 points in 5 dimensions.
4⁢x−1
27 908 0.250076752649 Henry Cohn, 2025, needs more optimization.
27 909 0.250084000707 Henry Cohn, 2025, needs more optimization.
27 910 0.250084783263 Henry Cohn, 2026, needs more optimization.
27 912 0.250095826107 Henry Cohn, 2026, needs more optimization.
27 913 0.250099713424 Henry Cohn, 2025, needs more optimization.
27 916 0.250106086370 Henry Cohn, 2026, needs more optimization.
27 917 0.250108530833 Henry Cohn, 2025, needs more optimization.
27 918 0.250312406419 Henry Cohn, 2026, needs more optimization.
27 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
28 57 0.028627089329 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
18928⁢x3−784⁢x2−28⁢x+1
28 58 0.033333333334 Henry Cohn, 2025.
30⁢x−1
28 59 0.042123224895 Henry Cohn, 2026, needs more optimization.
28 60 0.044207083554 Henry Cohn, 2026, needs more optimization.
28 61 0.044427604359 Henry Cohn, 2024, needs more optimization.
28 62 0.044625901428 Henry Cohn, 2024, needs more optimization.
28 63 0.045182176447 Henry Cohn, 2025.
28 64 0.045901657151 Henry Cohn, 2024, needs more optimization.
28 65 0.046144688998 Ilmari Vahteristo, 2026.
28 66 0.047459655819 Henry Cohn, 2026, needs more optimization.
28 67 0.052297853928 Henry Cohn, 2026, needs more optimization.
28 68 0.054257777968 Henry Cohn, 2026, needs more optimization.
28 69 0.056680407495 Henry Cohn, 2026, needs more optimization.
28 70 0.058160876266 Henry Cohn, 2026, needs more optimization.
28 71 0.059765758155 Ilmari Vahteristo, 2026.
28 72 0.061425534645 Ilmari Vahteristo, 2026.
28 73 0.063278585592 Ilmari Vahteristo, 2026.
28 74 0.064088659114 Henry Cohn, 2026, needs more optimization.
28 75 0.064460441711 Henry Cohn, 2026, needs more optimization.
28 76 0.065107470611 Henry Cohn, 2026, needs more optimization.
28 77 0.065929642936 Henry Cohn, 2026, needs more optimization.
28 78 0.067571589868 Henry Cohn, 2026, needs more optimization.
28 79 0.069484887075 Henry Cohn, 2026, needs more optimization.
28 80 0.070913702370 Henry Cohn, 2026, needs more optimization.
28 81 0.073507740052 Henry Cohn, 2026, needs more optimization.
28 82 0.074536648447 Henry Cohn, 2026, needs more optimization.
28 83 0.075219910127 Henry Cohn, 2026, needs more optimization.
28 84 0.075994545746 Henry Cohn, 2026, needs more optimization.
28 85 0.076729881285 Henry Cohn, 2026, needs more optimization.
28 86 0.076884539205 Henry Cohn, 2026, needs more optimization.
28 87 0.076915260604 Henry Cohn, 2026, needs more optimization.
28 88 0.076926982972 Henry Cohn, 2026, needs more optimization.
28 89 0.077242227162 Henry Cohn, 2026, needs more optimization.
28 90 0.077537204186 Henry Cohn, 2026, needs more optimization.
28 91 0.078294914190 Henry Cohn, 2026, needs more optimization.
28 92 0.078682990685 Henry Cohn, 2026, needs more optimization.
28 93 0.079255326328 Henry Cohn, 2026, needs more optimization.
28 94 0.079399741202 Henry Cohn, 2026, needs more optimization.
28 95 0.079800755584 Henry Cohn, 2026, needs more optimization.
28 96 0.080264484770 Henry Cohn, 2026, needs more optimization.
28 97 0.080284309797 Henry Cohn, 2026, needs more optimization.
28 98 0.080602285832 Henry Cohn, 2026, needs more optimization.
28 99 0.080659963159 Henry Cohn, 2026, needs more optimization.
28 100 0.080687070828 Henry Cohn, 2026, needs more optimization.
28 101 0.080688359983 Henry Cohn, 2026, needs more optimization.
28 102 0.083360350094 Henry Cohn, 2026, needs more optimization.
28 103 0.083873264391 Henry Cohn, 2026, needs more optimization.
28 104 0.086875118016 Henry Cohn, 2026, needs more optimization.
28 105 0.087840861269 Henry Cohn, 2026, needs more optimization.
28 106 0.088357351815 Henry Cohn, 2026, needs more optimization.
28 107 0.089042600663 Henry Cohn, 2026, needs more optimization.
28 108 0.089298537653 Henry Cohn, 2026, needs more optimization.
28 109 0.089614249411 Henry Cohn, 2026, needs more optimization.
28 110 0.090176565566 Henry Cohn, 2026, needs more optimization.
28 111 0.090382410672 Henry Cohn, 2026, needs more optimization.
28 112 0.090398986837 Henry Cohn, 2026, needs more optimization.
28 113 0.090572923262 Henry Cohn, 2026, needs more optimization.
28 114 0.090676108519 Henry Cohn, 2026, needs more optimization.
28 115 0.090789266517 Henry Cohn, 2026, needs more optimization.
28 116 0.090891787795 Henry Cohn, 2026, needs more optimization.
28 117 0.090909736756 Henry Cohn, 2026, needs more optimization.
28 118 0.091675659728 Henry Cohn, 2026, needs more optimization.
28 119 0.094587150633 Henry Cohn, 2026, needs more optimization.
28 120 0.096255191733 Henry Cohn, 2026, needs more optimization.
28 121 0.098148937279 Henry Cohn, 2026, needs more optimization.
28 122 0.099654964286 Henry Cohn, 2026, needs more optimization.
28 123 0.101805947778 Henry Cohn, 2026, needs more optimization.
28 124 0.102878763691 Henry Cohn, 2026, needs more optimization.
28 125 0.103068782625 Henry Cohn, 2026, needs more optimization.
28 129 0.103122315456 Henry Cohn, 2026, needs more optimization.
28 130 0.103589055879 Henry Cohn, 2026, needs more optimization.
28 131 0.104419960229 Henry Cohn, 2026, needs more optimization.
28 132 0.105963013313 Henry Cohn, 2026, needs more optimization.
28 133 0.106279459263 Henry Cohn, 2026, needs more optimization.
28 134 0.108139525644 Henry Cohn, 2026, needs more optimization.
28 135 0.108634810438 Henry Cohn, 2026, needs more optimization.
28 136 0.109592328265 Henry Cohn, 2026, needs more optimization.
28 137 0.110291432201 Henry Cohn, 2026, needs more optimization.
28 138 0.110916127060 Henry Cohn, 2026, needs more optimization.
28 139 0.110935533256 Henry Cohn, 2026, needs more optimization.
28 140 0.111841871134 Henry Cohn, 2026, needs more optimization.
28 141 0.112429224658 Henry Cohn, 2026, needs more optimization.
28 142 0.113895832004 Henry Cohn, 2026, needs more optimization.
28 143 0.115284246218 Henry Cohn, 2026, needs more optimization.
28 144 0.116179512953 Henry Cohn, 2026, needs more optimization.
28 145 0.117183850175 Henry Cohn, 2026, needs more optimization.
28 146 0.117979608661 Henry Cohn, 2026, needs more optimization.
28 147 0.119198839866 Henry Cohn, 2026, needs more optimization.
28 148 0.120739405837 Henry Cohn, 2026, needs more optimization.
28 149 0.121669146845 Henry Cohn, 2026, needs more optimization.
28 150 0.122936589991 Henry Cohn, 2026, needs more optimization.
28 151 0.124463032964 Henry Cohn, 2026, needs more optimization.
28 152 0.125864134494 Henry Cohn, 2026, needs more optimization.
28 153 0.126664383231 Henry Cohn, 2026, needs more optimization.
28 154 0.128219317009 Henry Cohn, 2026, needs more optimization.
28 155 0.129192610893 Henry Cohn, 2026, needs more optimization.
28 156 0.131004770279 Henry Cohn, 2026, needs more optimization.
28 157 0.131490147907 Henry Cohn, 2026, needs more optimization.
28 158 0.131591590046 Henry Cohn, 2026, needs more optimization.
28 159 0.131926839997 Henry Cohn, 2026, needs more optimization.
28 160 0.132064592699 Henry Cohn, 2026, needs more optimization.
28 161 0.132297650228 Henry Cohn, 2026, needs more optimization.
28 162 0.132517743322 Henry Cohn, 2026, needs more optimization.
28 163 0.132722182838 Henry Cohn, 2026, needs more optimization.
28 164 0.132815247590 Henry Cohn, 2026, needs more optimization.
28 165 0.133021234764 Henry Cohn, 2026, needs more optimization.
28 166 0.133177322883 Henry Cohn, 2026, needs more optimization.
28 167 0.133200804972 Henry Cohn, 2026, needs more optimization.
28 168 0.133252804086 Henry Cohn, 2026, needs more optimization.
28 169 0.133307200648 Henry Cohn, 2026, needs more optimization.
28 170 0.133812055331 Henry Cohn, 2026, needs more optimization.
28 171 0.135008313893 Henry Cohn, 2026, needs more optimization.
28 172 0.135087616953 Henry Cohn, 2026, needs more optimization.
28 173 0.135093910815 Henry Cohn, 2026, needs more optimization.
28 174 0.135111946819 Henry Cohn, 2026, needs more optimization.
28 175 0.135133816514 Henry Cohn, 2026, needs more optimization.
28 176 0.135431147197 Henry Cohn, 2026, needs more optimization.
28 177 0.135831971961 Henry Cohn, 2026, needs more optimization.
28 178 0.136198258931 Henry Cohn, 2026, needs more optimization.
28 179 0.137093999438 Henry Cohn, 2026, needs more optimization.
28 180 0.138120626454 Henry Cohn, 2026, needs more optimization.
28 181 0.138965214796 Henry Cohn, 2026, needs more optimization.
28 182 0.139736552190 Henry Cohn, 2026, needs more optimization.
28 183 0.140843833772 Henry Cohn, 2026, needs more optimization.
28 184 0.142337499902 Henry Cohn, 2026, needs more optimization.
28 187 0.142347532788 Henry Cohn, 2026, needs more optimization.
28 189 0.142402904503 Henry Cohn, 2026, needs more optimization.
28 190 0.142444530319 Henry Cohn, 2026, needs more optimization.
28 191 0.142458957331 Henry Cohn, 2026, needs more optimization.
28 192 0.142570810396 Henry Cohn, 2026, needs more optimization.
28 193 0.142608475421 Henry Cohn, 2026, needs more optimization.
28 194 0.142653858420 Henry Cohn, 2026, needs more optimization.
28 195 0.142729283197 Henry Cohn, 2026, needs more optimization.
28 196 0.142767752948 Henry Cohn, 2026, needs more optimization.
28 198 0.142845136371 Henry Cohn, 2026, needs more optimization.
28 199 0.143023475605 Henry Cohn, 2026, needs more optimization.
28 200 0.143384638181 Henry Cohn, 2026, needs more optimization.
28 201 0.143879484424 Henry Cohn, 2026, needs more optimization.
28 202 0.144264140230 Henry Cohn, 2026, needs more optimization.
28 203 0.145128242910 Henry Cohn, 2026, needs more optimization.
28 204 0.145981090303 Henry Cohn, 2026, needs more optimization.
28 205 0.146246337867 Henry Cohn, 2026, needs more optimization.
28 206 0.147410392601 Henry Cohn, 2026, needs more optimization.
28 207 0.148510956466 Henry Cohn, 2026, needs more optimization.
28 209 0.148882443232 Henry Cohn, 2026, needs more optimization.
28 210 0.148958481245 Henry Cohn, 2026, needs more optimization.
28 211 0.149045953846 Henry Cohn, 2026, needs more optimization.
28 212 0.149728592136 Henry Cohn, 2026, needs more optimization.
28 213 0.149983415923 Henry Cohn, 2026, needs more optimization.
28 214 0.150361520122 Henry Cohn, 2026, needs more optimization.
28 215 0.151214544350 Henry Cohn, 2026, needs more optimization.
28 216 0.151808054785 Henry Cohn, 2026, needs more optimization.
28 217 0.151993340985 Henry Cohn, 2026, needs more optimization.
28 218 0.152450869279 Henry Cohn, 2026, needs more optimization.
28 219 0.152881101006 Henry Cohn, 2026, needs more optimization.
28 220 0.157009083578 Henry Cohn, 2026, needs more optimization.
28 221 0.157142801704 Henry Cohn, 2026, needs more optimization.
28 222 0.158046718212 Henry Cohn, 2026, needs more optimization.
28 223 0.160336267452 Henry Cohn, 2026, needs more optimization.
28 224 0.160789746370 Henry Cohn, 2026, needs more optimization.
28 225 0.160848602787 Henry Cohn, 2026, needs more optimization.
28 226 0.160888717937 Henry Cohn, 2026, needs more optimization.
28 227 0.160931661133 Henry Cohn, 2026, needs more optimization.
28 228 0.160968219374 Henry Cohn, 2026, needs more optimization.
28 229 0.161006073936 Henry Cohn, 2026, needs more optimization.
28 230 0.161048780296 Henry Cohn, 2026, needs more optimization.
28 231 0.161087023664 Henry Cohn, 2026, needs more optimization.
28 232 0.161132806026 Henry Cohn, 2026, needs more optimization.
28 233 0.161483563029 Henry Cohn, 2026, needs more optimization.
28 234 0.161509251075 Henry Cohn, 2026, needs more optimization.
28 235 0.161535309467 Henry Cohn, 2026, needs more optimization.
28 236 0.161556789150 Henry Cohn, 2026, needs more optimization.
28 237 0.161591069550 Henry Cohn, 2026, needs more optimization.
28 238 0.161619857688 Henry Cohn, 2026, needs more optimization.
28 241 0.161627723805 Henry Cohn, 2026, needs more optimization.
28 242 0.161735964206 Henry Cohn, 2026, needs more optimization.
28 243 0.161741064087 Henry Cohn, 2026, needs more optimization.
28 244 0.161805154606 Henry Cohn, 2026, needs more optimization.
28 246 0.161805154743 Henry Cohn, 2026, needs more optimization.
28 248 0.161856039522 Henry Cohn, 2026, needs more optimization.
28 249 0.163075265595 Henry Cohn, 2026, needs more optimization.
28 250 0.163850639744 Henry Cohn, 2026, needs more optimization.
28 251 0.164323610767 Henry Cohn, 2026, needs more optimization.
28 256 0.165809729546 Henry Cohn, 2026, needs more optimization.
28 259 0.165956761111 Henry Cohn, 2026, needs more optimization.
28 260 0.166078880574 Henry Cohn, 2026, needs more optimization.
28 261 0.166096002858 Henry Cohn, 2026, needs more optimization.
28 264 0.166136116761 Henry Cohn, 2026, needs more optimization.
28 267 0.166367400121 Henry Cohn, 2026, needs more optimization.
28 290 0.166666666667 Orthogonal union of 275 points in 22 dimensions and 15 points in 6 dimensions.
6⁢x−1
28 291 0.166696111005 Orthogonal union of 289 points in 27 dimensions and 2 points in 1 dimension.
28 292 0.177070882269 Henry Cohn, 2026, needs more optimization.
28 293 0.177434181065 Henry Cohn, 2026, needs more optimization.
28 294 0.179493118776 Orthogonal union of 292 points in 27 dimensions and 2 points in 1 dimension.
28 295 0.179493566291 Orthogonal union of 293 points in 27 dimensions and 2 points in 1 dimension.
28 296 0.179493965203 Orthogonal union of 294 points in 27 dimensions and 2 points in 1 dimension.
28 298 0.179494072201 Henry Cohn, 2026, needs more optimization.
28 299 0.179494792438 Henry Cohn, 2026, needs more optimization.
28 300 0.179495671503 Henry Cohn, 2026, needs more optimization.
28 301 0.179498235412 Orthogonal union of 299 points in 27 dimensions and 2 points in 1 dimension.
28 302 0.179500637410 Orthogonal union of 300 points in 27 dimensions and 2 points in 1 dimension.
28 304 0.179540025559 Henry Cohn, 2026, needs more optimization.
28 305 0.179556400032 Henry Cohn, 2026, needs more optimization.
28 306 0.179721772975 Henry Cohn, 2026, needs more optimization.
28 307 0.181818181819 Orthogonal union of 297 points in 24 dimensions and 10 points in 4 dimensions.
11⁢x−2
28 314 0.193548387073 Henry Cohn, 2026, needs more optimization.
28 338 0.193548387074 Henry Cohn, 2026, needs more optimization.
28 340 0.193548387097 Orthogonal union of 330 points in 24 dimensions and 10 points in 4 dimensions.
31⁢x−6
28 344 0.195656419106 Henry Cohn, 2026, needs more optimization.
28 348 0.195814847231 Henry Cohn, 2026, needs more optimization.
28 350 0.196890169770 Henry Cohn, 2026, needs more optimization.
28 352 0.196890169936 Henry Cohn, 2026, needs more optimization.
28 356 0.196954209571 Henry Cohn, 2026, needs more optimization.
28 359 0.199999943719 Henry Cohn, 2026, needs more optimization.
28 568 0.2 Orthogonal union of 552 points in 23 dimensions and 16 points in 5 dimensions.
5⁢x−1
28 570 0.200116970684 Henry Cohn, 2026, needs more optimization.
28 572 0.237569013471 Henry Cohn, 2026, needs more optimization.
28 575 0.237590051282 Henry Cohn, 2025, needs more optimization.
28 576 0.237597962608 Henry Cohn, 2026, needs more optimization.
28 578 0.237610957097 Henry Cohn, 2026, needs more optimization.
28 579 0.237628473124 Henry Cohn, 2026, needs more optimization.
28 580 0.237629619918 Henry Cohn, 2026, needs more optimization.
28 581 0.237692814107 Henry Cohn, 2026, needs more optimization.
28 582 0.237714075083 Henry Cohn, 2025, needs more optimization.
28 584 0.237716304844 Henry Cohn, 2026, needs more optimization.
28 588 0.238072292146 Henry Cohn, 2026, needs more optimization.
28 596 0.238101495092 Henry Cohn, 2026, needs more optimization.
28 604 0.238133418950 Henry Cohn, 2026, needs more optimization.
28 612 0.238188262156 Henry Cohn, 2026, needs more optimization.
28 620 0.238395994479 Henry Cohn, 2026, needs more optimization.
28 628 0.239141579031 Henry Cohn, 2026, needs more optimization.
28 632 0.241077615809 Henry Cohn, 2026, needs more optimization.
28 636 0.241508043760 Henry Cohn, 2026, needs more optimization.
28 640 0.244245435854 Henry Cohn, 2026, needs more optimization.
28 644 0.245037071683 Henry Cohn, 2026, needs more optimization.
28 652 0.246038453780 Henry Cohn, 2026, needs more optimization.
28 660 0.246818081010 Henry Cohn, 2026, needs more optimization.
28 668 0.247406464596 Henry Cohn, 2026, needs more optimization.
28 686 0.247642877690 Henry Cohn, 2026, needs more optimization.
28 690 0.247884804283 Henry Cohn, 2026, needs more optimization.
28 694 0.248162276651 Henry Cohn, 2026, needs more optimization.
28 698 0.248427892029 Henry Cohn, 2026, needs more optimization.
28 702 0.248693811168 Henry Cohn, 2026, needs more optimization.
28 706 0.248950450030 Henry Cohn, 2026, needs more optimization.
28 710 0.249208911690 Henry Cohn, 2026, needs more optimization.
28 714 0.249432174846 Henry Cohn, 2026, needs more optimization.
28 718 0.249630071155 Henry Cohn, 2026, needs more optimization.
28 722 0.249790919034 Henry Cohn, 2026, needs more optimization.
28 724 0.249896901858 Henry Cohn, 2026, needs more optimization.
28 945 0.25 Henry Cohn, 2026.
4⁢x−1
28 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
29 59 0.027727451354 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
21141⁢x3−841⁢x2−29⁢x+1
29 60 0.032283994156 Henry Cohn, 2024.
29 61 0.040902439084 Ilmari Vahteristo, 2026.
29 62 0.043321650170 Henry Cohn, 2026, needs more optimization.
29 63 0.043679238443 Henry Cohn, 2026, needs more optimization.
29 64 0.044358604455 Henry Cohn, 2026, needs more optimization.
29 65 0.044606014654 Henry Cohn, 2026, needs more optimization.
29 66 0.044624560381 Henry Cohn, 2026, needs more optimization.
29 67 0.044634959655 Ilmari Vahteristo, 2026.
29 68 0.046023775811 Henry Cohn, 2026, needs more optimization.
29 69 0.050838211862 Henry Cohn, 2026, needs more optimization.
29 70 0.053009019447 Henry Cohn, 2026, needs more optimization.
29 71 0.054294848325 Henry Cohn, 2026, needs more optimization.
29 72 0.056580879549 Ilmari Vahteristo, 2026.
29 73 0.057725039415 Henry Cohn, 2026, needs more optimization.
29 74 0.059425484827 Ilmari Vahteristo, 2026.
29 75 0.061018195925 Ilmari Vahteristo, 2026.
29 76 0.062685332560 Ilmari Vahteristo, 2026.
29 77 0.063118781133 Henry Cohn, 2026, needs more optimization.
29 78 0.063580262622 Henry Cohn, 2026, needs more optimization.
29 79 0.064149508910 Henry Cohn, 2026, needs more optimization.
29 80 0.065731224072 Henry Cohn, 2026, needs more optimization.
29 81 0.067257843250 Henry Cohn, 2026, needs more optimization.
29 82 0.069106145536 Henry Cohn, 2026, needs more optimization.
29 83 0.070359470518 Henry Cohn, 2026, needs more optimization.
29 84 0.072182192822 Henry Cohn, 2026, needs more optimization.
29 85 0.073572105168 Henry Cohn, 2026, needs more optimization.
29 86 0.074839660492 Henry Cohn, 2026, needs more optimization.
29 87 0.075746825917 Henry Cohn, 2026, needs more optimization.
29 88 0.076262869100 Henry Cohn, 2026, needs more optimization.
29 89 0.076456235217 Henry Cohn, 2026, needs more optimization.
29 90 0.076802878012 Henry Cohn, 2026, needs more optimization.
29 91 0.076986014503 Henry Cohn, 2026, needs more optimization.
29 92 0.077171106453 Henry Cohn, 2026, needs more optimization.
29 93 0.077401578944 Henry Cohn, 2026, needs more optimization.
29 94 0.077934442858 Henry Cohn, 2026, needs more optimization.
29 95 0.078080044562 Henry Cohn, 2026, needs more optimization.
29 96 0.078171353380 Henry Cohn, 2026, needs more optimization.
29 97 0.078819540834 Henry Cohn, 2026, needs more optimization.
29 98 0.078883077025 Henry Cohn, 2026, needs more optimization.
29 99 0.079122379005 Henry Cohn, 2026, needs more optimization.
29 100 0.079421808113 Henry Cohn, 2026, needs more optimization.
29 101 0.080120971957 Henry Cohn, 2026, needs more optimization.
29 102 0.080578617225 Henry Cohn, 2026, needs more optimization.
29 103 0.080684427737 Henry Cohn, 2026, needs more optimization.
29 104 0.080688916720 Henry Cohn, 2026, needs more optimization.
29 105 0.080839484024 Henry Cohn, 2026, needs more optimization.
29 106 0.083844983361 Henry Cohn, 2026, needs more optimization.
29 107 0.084055404834 Henry Cohn, 2026, needs more optimization.
29 112 0.086333380579 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001, Example 5.10.1.
111⁢x2+2⁢x−1
29 113 0.089757553696 Henry Cohn, 2026, needs more optimization.
29 114 0.089843804795 Henry Cohn, 2026, needs more optimization.
29 115 0.089940094957 Henry Cohn, 2026, needs more optimization.
29 116 0.090088119123 Henry Cohn, 2026, needs more optimization.
29 117 0.090304375906 Henry Cohn, 2026, needs more optimization.
29 118 0.090583603889 Henry Cohn, 2026, needs more optimization.
29 119 0.090787470282 Henry Cohn, 2026, needs more optimization.
29 120 0.090870157470 Henry Cohn, 2026, needs more optimization.
29 121 0.091123624631 Henry Cohn, 2026, needs more optimization.
29 122 0.091985338205 Henry Cohn, 2026, needs more optimization.
29 123 0.094082575227 Henry Cohn, 2026, needs more optimization.
29 124 0.094254725843 Henry Cohn, 2026, needs more optimization.
29 125 0.096614678626 Henry Cohn, 2026, needs more optimization.
29 126 0.098458673212 Henry Cohn, 2026, needs more optimization.
29 127 0.100092681919 Henry Cohn, 2026, needs more optimization.
29 128 0.101514436646 Henry Cohn, 2026, needs more optimization.
29 130 0.102457215481 Henry Cohn, 2026, needs more optimization.
29 131 0.102601401439 Henry Cohn, 2026, needs more optimization.
29 132 0.102908787260 Henry Cohn, 2026, needs more optimization.
29 133 0.102982107446 Henry Cohn, 2026, needs more optimization.
29 134 0.103022646978 Henry Cohn, 2026, needs more optimization.
29 135 0.103129995114 Henry Cohn, 2026, needs more optimization.
29 136 0.103853518140 Henry Cohn, 2026, needs more optimization.
29 137 0.105576868033 Henry Cohn, 2026, needs more optimization.
29 138 0.106936076895 Henry Cohn, 2026, needs more optimization.
29 139 0.107582591516 Henry Cohn, 2026, needs more optimization.
29 140 0.108487734788 Henry Cohn, 2026, needs more optimization.
29 141 0.109326411502 Henry Cohn, 2026, needs more optimization.
29 142 0.110355691465 Henry Cohn, 2026, needs more optimization.
29 143 0.110516659226 Henry Cohn, 2026, needs more optimization.
29 144 0.110745679049 Henry Cohn, 2026, needs more optimization.
29 145 0.110906904805 Henry Cohn, 2026, needs more optimization.
29 146 0.111264533677 Henry Cohn, 2026, needs more optimization.
29 147 0.111390686249 Henry Cohn, 2026, needs more optimization.
29 148 0.112364223551 Henry Cohn, 2026, needs more optimization.
29 149 0.114442084961 Henry Cohn, 2026, needs more optimization.
29 150 0.115378760583 Henry Cohn, 2026, needs more optimization.
29 151 0.116263608053 Henry Cohn, 2026, needs more optimization.
29 152 0.116962974033 Henry Cohn, 2026, needs more optimization.
29 153 0.118402654499 Henry Cohn, 2026, needs more optimization.
29 154 0.119134678965 Henry Cohn, 2026, needs more optimization.
29 155 0.120125980611 Henry Cohn, 2026, needs more optimization.
29 156 0.121120865439 Henry Cohn, 2026, needs more optimization.
29 157 0.122326161149 Henry Cohn, 2026, needs more optimization.
29 158 0.123124288777 Henry Cohn, 2026, needs more optimization.
29 159 0.124379562441 Henry Cohn, 2026, needs more optimization.
29 160 0.125451389202 Henry Cohn, 2026, needs more optimization.
29 162 0.127297587558 Henry Cohn, 2026, needs more optimization.
29 163 0.127941576577 Henry Cohn, 2026, needs more optimization.
29 164 0.128083991332 Henry Cohn, 2026, needs more optimization.
29 165 0.128153898965 Henry Cohn, 2026, needs more optimization.
29 166 0.128304719170 Henry Cohn, 2026, needs more optimization.
29 167 0.128422786138 Henry Cohn, 2026, needs more optimization.
29 168 0.129230989963 Henry Cohn, 2026, needs more optimization.
29 169 0.129869344342 Henry Cohn, 2026, needs more optimization.
29 170 0.131579856642 Henry Cohn, 2026, needs more optimization.
29 171 0.132343627390 Henry Cohn, 2026, needs more optimization.
29 172 0.132617475509 Henry Cohn, 2026, needs more optimization.
29 173 0.132777098940 Henry Cohn, 2026, needs more optimization.
29 174 0.133096585370 Henry Cohn, 2026, needs more optimization.
29 175 0.133190300982 Henry Cohn, 2026, needs more optimization.
29 176 0.133382816064 Henry Cohn, 2026, needs more optimization.
29 177 0.134083797565 Henry Cohn, 2026, needs more optimization.
29 178 0.134815753242 Henry Cohn, 2026, needs more optimization.
29 179 0.134819145710 Henry Cohn, 2026, needs more optimization.
29 180 0.134910627703 Henry Cohn, 2026, needs more optimization.
29 181 0.135066437698 Henry Cohn, 2026, needs more optimization.
29 182 0.135160186470 Henry Cohn, 2026, needs more optimization.
29 183 0.135509382661 Henry Cohn, 2026, needs more optimization.
29 184 0.135701293701 Henry Cohn, 2026, needs more optimization.
29 185 0.136672649206 Henry Cohn, 2026, needs more optimization.
29 186 0.136815871252 Henry Cohn, 2026, needs more optimization.
29 187 0.137471040907 Henry Cohn, 2026, needs more optimization.
29 188 0.138229268114 Henry Cohn, 2026, needs more optimization.
29 189 0.139510153134 Henry Cohn, 2026, needs more optimization.
29 190 0.140142982780 Henry Cohn, 2026, needs more optimization.
29 191 0.141058975939 Henry Cohn, 2026, needs more optimization.
29 192 0.141549137470 Henry Cohn, 2026, needs more optimization.
29 193 0.141789194992 Henry Cohn, 2026, needs more optimization.
29 194 0.142008222731 Henry Cohn, 2026, needs more optimization.
29 195 0.142122714305 Henry Cohn, 2026, needs more optimization.
29 196 0.142153101175 Henry Cohn, 2026, needs more optimization.
29 197 0.142196306785 Henry Cohn, 2026, needs more optimization.
29 198 0.142257183171 Henry Cohn, 2026, needs more optimization.
29 199 0.142283237495 Henry Cohn, 2026, needs more optimization.
29 200 0.142340285349 Henry Cohn, 2026, needs more optimization.
29 201 0.142421528091 Henry Cohn, 2026, needs more optimization.
29 202 0.142474395480 Henry Cohn, 2026, needs more optimization.
29 203 0.142509991530 Henry Cohn, 2026, needs more optimization.
29 204 0.142579473678 Henry Cohn, 2026, needs more optimization.
29 205 0.142653131218 Henry Cohn, 2026, needs more optimization.
29 206 0.142768966102 Henry Cohn, 2026, needs more optimization.
29 207 0.142963009616 Henry Cohn, 2026, needs more optimization.
29 208 0.143117030567 Henry Cohn, 2026, needs more optimization.
29 209 0.143562328582 Henry Cohn, 2026, needs more optimization.
29 210 0.143857306343 Henry Cohn, 2026, needs more optimization.
29 211 0.144556053110 Henry Cohn, 2026, needs more optimization.
29 212 0.144996401879 Henry Cohn, 2026, needs more optimization.
29 213 0.145555877949 Henry Cohn, 2026, needs more optimization.
29 214 0.145969104797 Henry Cohn, 2026, needs more optimization.
29 215 0.147039610796 Henry Cohn, 2026, needs more optimization.
29 216 0.148051172055 Henry Cohn, 2026, needs more optimization.
29 217 0.148564735200 Henry Cohn, 2026, needs more optimization.
29 218 0.148736578891 Henry Cohn, 2026, needs more optimization.
29 219 0.148936748716 Henry Cohn, 2026, needs more optimization.
29 220 0.149277800939 Henry Cohn, 2026, needs more optimization.
29 221 0.149359469023 Henry Cohn, 2026, needs more optimization.
29 222 0.150271805195 Henry Cohn, 2026, needs more optimization.
29 223 0.151376567278 Henry Cohn, 2026, needs more optimization.
29 224 0.157792007743 Henry Cohn, 2026, needs more optimization.
29 225 0.158520992303 Henry Cohn, 2026, needs more optimization.
29 226 0.158614196833 Henry Cohn, 2026, needs more optimization.
29 227 0.158636702904 Henry Cohn, 2026, needs more optimization.
29 228 0.158741397775 Henry Cohn, 2026, needs more optimization.
29 229 0.158798185069 Henry Cohn, 2026, needs more optimization.
29 230 0.158979668295 Henry Cohn, 2026, needs more optimization.
29 231 0.159263289806 Henry Cohn, 2026, needs more optimization.
29 232 0.159388738588 Henry Cohn, 2026, needs more optimization.
29 233 0.159755416603 Henry Cohn, 2026, needs more optimization.
29 235 0.159936513481 Henry Cohn, 2026, needs more optimization.
29 236 0.160079733993 Henry Cohn, 2026, needs more optimization.
29 237 0.160221329145 Henry Cohn, 2026, needs more optimization.
29 240 0.160475104220 Henry Cohn, 2026, needs more optimization.
29 241 0.160618460240 Henry Cohn, 2026, needs more optimization.
29 244 0.160815568094 Henry Cohn, 2026, needs more optimization.
29 245 0.160946930924 Henry Cohn, 2026, needs more optimization.
29 247 0.161109976308 Henry Cohn, 2026, needs more optimization.
29 250 0.161395387145 Henry Cohn, 2026, needs more optimization.
29 251 0.162102529586 Henry Cohn, 2026, needs more optimization.
29 252 0.162513266043 Henry Cohn, 2026, needs more optimization.
29 253 0.162611411800 Henry Cohn, 2026, needs more optimization.
29 254 0.162727880600 Henry Cohn, 2026, needs more optimization.
29 256 0.162853060469 Henry Cohn, 2026, needs more optimization.
29 257 0.163075299559 Henry Cohn, 2026, needs more optimization.
29 258 0.163090450261 Henry Cohn, 2026, needs more optimization.
29 259 0.163097347857 Henry Cohn, 2026, needs more optimization.
29 260 0.163107531292 Henry Cohn, 2026, needs more optimization.
29 262 0.163243181453 Henry Cohn, 2026, needs more optimization.
29 263 0.163360276104 Henry Cohn, 2026, needs more optimization.
29 265 0.163508341785 Henry Cohn, 2026, needs more optimization.
29 268 0.163571298625 Henry Cohn, 2026, needs more optimization.
29 269 0.163684033131 Henry Cohn, 2026, needs more optimization.
29 270 0.164048277666 Henry Cohn, 2026, needs more optimization.
29 271 0.164150360669 Henry Cohn, 2026, needs more optimization.
29 272 0.164322412957 Henry Cohn, 2026, needs more optimization.
29 273 0.164443779536 Henry Cohn, 2026, needs more optimization.
29 274 0.164680727534 Henry Cohn, 2026, needs more optimization.
29 275 0.164920743984 Henry Cohn, 2026, needs more optimization.
29 276 0.165217774917 Henry Cohn, 2026, needs more optimization.
29 277 0.165366512551 Henry Cohn, 2026, needs more optimization.
29 278 0.165708641240 Henry Cohn, 2026, needs more optimization.
29 279 0.165973399728 Henry Cohn, 2026, needs more optimization.
29 280 0.166426723110 Henry Cohn, 2026, needs more optimization.
29 281 0.166434973048 Henry Cohn, 2026, needs more optimization.
29 282 0.166443297326 Henry Cohn, 2026, needs more optimization.
29 283 0.166451362284 Henry Cohn, 2026, needs more optimization.
29 284 0.166460123388 Henry Cohn, 2026, needs more optimization.
29 285 0.166470647712 Henry Cohn, 2026, needs more optimization.
29 286 0.166484653796 Henry Cohn, 2026, needs more optimization.
29 287 0.166610722787 Henry Cohn, 2026, needs more optimization.
29 288 0.166612878295 Henry Cohn, 2026, needs more optimization.
29 289 0.166614956907 Henry Cohn, 2026, needs more optimization.
29 290 0.166616986969 Henry Cohn, 2026, needs more optimization.
29 291 0.166619570891 Henry Cohn, 2026, needs more optimization.
29 292 0.166621958488 Henry Cohn, 2026, needs more optimization.
29 293 0.166624289278 Henry Cohn, 2026, needs more optimization.
29 294 0.166626957914 Henry Cohn, 2026, needs more optimization.
29 295 0.166630009342 Henry Cohn, 2026, needs more optimization.
29 296 0.166633355804 Henry Cohn, 2026, needs more optimization.
29 297 0.166637875888 Henry Cohn, 2026, needs more optimization.
29 298 0.166641962421 Henry Cohn, 2026, needs more optimization.
29 299 0.166645655945 Henry Cohn, 2026, needs more optimization.
29 300 0.166649699367 Henry Cohn, 2026, needs more optimization.
29 301 0.166681308189 Henry Cohn, 2026, needs more optimization.
29 304 0.176498297560 Henry Cohn, 2026, needs more optimization.
29 305 0.176505613813 Henry Cohn, 2025, needs more optimization.
29 306 0.176545037841 Henry Cohn, 2026, needs more optimization.
29 307 0.176625904401 Henry Cohn, 2026, needs more optimization.
29 308 0.177158896376 Henry Cohn, 2026, needs more optimization.
29 309 0.178795972454 Henry Cohn, 2025, needs more optimization.
29 310 0.179391364267 Henry Cohn, 2025, needs more optimization.
29 316 0.184844380513 Henry Cohn, 2026, needs more optimization.
29 323 0.186920334129 Henry Cohn, 2026, needs more optimization.
29 324 0.186920334378 Henry Cohn, 2026, needs more optimization.
29 332 0.188266577612 Henry Cohn, 2026, needs more optimization.
29 340 0.190086978757 Henry Cohn, 2026, needs more optimization.
29 348 0.191573393268 Henry Cohn, 2026, needs more optimization.
29 356 0.192794409597 Henry Cohn, 2026, needs more optimization.
29 360 0.193991725221 Henry Cohn, 2026, needs more optimization.
29 364 0.194744498195 Henry Cohn, 2026, needs more optimization.
29 372 0.195727991829 Henry Cohn, 2026, needs more optimization.
29 376 0.196771724184 Henry Cohn, 2026, needs more optimization.
29 379 0.199999985172 Henry Cohn, 2026, needs more optimization.
29 570 0.2 Orthogonal union of 552 points in 23 dimensions and 18 points in 6 dimensions.
5⁢x−1
29 572 0.200055249226 Henry Cohn, 2026, needs more optimization.
29 575 0.200056882243 Henry Cohn, 2026, needs more optimization.
29 577 0.200056900350 Henry Cohn, 2026, needs more optimization.
29 580 0.200061881180 Henry Cohn, 2025, needs more optimization.
29 583 0.200084219050 Henry Cohn, 2026, needs more optimization.
29 584 0.200099371985 Henry Cohn, 2026, needs more optimization.
29 585 0.235221457188 Henry Cohn, 2026, needs more optimization.
29 586 0.235624165467 Henry Cohn, 2026, needs more optimization.
29 587 0.235648905409 Henry Cohn, 2026, needs more optimization.
29 588 0.235654509680 Henry Cohn, 2026, needs more optimization.
29 589 0.235745981170 Henry Cohn, 2026, needs more optimization.
29 590 0.235925600017 Henry Cohn, 2026, needs more optimization.
29 591 0.236072283800 Henry Cohn, 2026, needs more optimization.
29 592 0.236109405881 Henry Cohn, 2026, needs more optimization.
29 593 0.236190721234 Henry Cohn, 2026, needs more optimization.
29 594 0.236190721353 Henry Cohn, 2026, needs more optimization.
29 595 0.236228408721 Henry Cohn, 2026, needs more optimization.
29 596 0.236233830934 Henry Cohn, 2026, needs more optimization.
29 597 0.236299967472 Henry Cohn, 2026, needs more optimization.
29 598 0.236348373451 Henry Cohn, 2026, needs more optimization.
29 599 0.236476403828 Henry Cohn, 2026, needs more optimization.
29 600 0.236655990754 Henry Cohn, 2026, needs more optimization.
29 602 0.236707974235 Henry Cohn, 2026, needs more optimization.
29 603 0.236746113239 Henry Cohn, 2026, needs more optimization.
29 604 0.236755244569 Henry Cohn, 2026, needs more optimization.
29 605 0.236792082737 Henry Cohn, 2026, needs more optimization.
29 606 0.236889761101 Henry Cohn, 2026, needs more optimization.
29 607 0.237573215381 Henry Cohn, 2026, needs more optimization.
29 608 0.237579102548 Henry Cohn, 2026, needs more optimization.
29 609 0.237806711978 Henry Cohn, 2026, needs more optimization.
29 612 0.237999515348 Henry Cohn, 2026, needs more optimization.
29 620 0.238053596052 Henry Cohn, 2026, needs more optimization.
29 628 0.238114041981 Henry Cohn, 2026, needs more optimization.
29 632 0.238266310179 Henry Cohn, 2026, needs more optimization.
29 636 0.238294864888 Henry Cohn, 2026, needs more optimization.
29 640 0.239119677104 Henry Cohn, 2026, needs more optimization.
29 644 0.242764941664 Henry Cohn, 2026, needs more optimization.
29 652 0.244065241831 Henry Cohn, 2026, needs more optimization.
29 660 0.245112529344 Henry Cohn, 2026, needs more optimization.
29 668 0.245962641511 Henry Cohn, 2026, needs more optimization.
29 686 0.245963097698 Henry Cohn, 2026, needs more optimization.
29 690 0.246263066045 Henry Cohn, 2026, needs more optimization.
29 694 0.246559229535 Henry Cohn, 2026, needs more optimization.
29 698 0.246836547318 Henry Cohn, 2026, needs more optimization.
29 702 0.247108921213 Henry Cohn, 2026, needs more optimization.
29 706 0.247362161736 Henry Cohn, 2026, needs more optimization.
29 710 0.247615143709 Henry Cohn, 2026, needs more optimization.
29 714 0.247850231105 Henry Cohn, 2026, needs more optimization.
29 718 0.248074549071 Henry Cohn, 2026, needs more optimization.
29 722 0.248279372055 Henry Cohn, 2026, needs more optimization.
29 726 0.248490746134 Henry Cohn, 2026, needs more optimization.
29 730 0.248693949352 Henry Cohn, 2026, needs more optimization.
29 734 0.248912498099 Henry Cohn, 2026, needs more optimization.
29 738 0.249122568310 Henry Cohn, 2026, needs more optimization.
29 742 0.249320518369 Henry Cohn, 2026, needs more optimization.
29 746 0.249485466210 Henry Cohn, 2026, needs more optimization.
29 750 0.249631905302 Henry Cohn, 2026, needs more optimization.
29 754 0.249748723711 Henry Cohn, 2026, needs more optimization.
29 758 0.249836871909 Henry Cohn, 2026, needs more optimization.
29 762 0.249901313084 Henry Cohn, 2026, needs more optimization.
29 764 0.249948561778 Henry Cohn, 2026, needs more optimization.
29 766 0.249949288241 Henry Cohn, 2026, needs more optimization.
29 768 0.249983994111 Henry Cohn, 2026, needs more optimization.
29 769 0.249999521611 Henry Cohn, 2026, needs more optimization.
29 947 0.25 Orthogonal union of 945 points in 28 dimensions and 2 points in 1 dimension.
4⁢x−1
29 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
30 61 0.026884307091 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
23520⁢x3−900⁢x2−30⁢x+1
30 62 0.031274722522 Henry Cohn, 2026, needs more optimization.
30 63 0.039846497808 Ilmari Vahteristo, 2026.
30 64 0.041979616323 Henry Cohn, 2026, needs more optimization.
30 65 0.043476230860 Henry Cohn, 2026, needs more optimization.
30 66 0.044301112855 Henry Cohn, 2026, needs more optimization.
30 67 0.044456014538 Henry Cohn, 2026, needs more optimization.
30 68 0.044556632084 Henry Cohn, 2026, needs more optimization.
30 69 0.044563869603 Ilmari Vahteristo, 2026.
30 70 0.044757477298 Henry Cohn, 2026, needs more optimization.
30 71 0.049847240264 Ilmari Vahteristo, 2026.
30 72 0.051437951998 Ilmari Vahteristo, 2026.
30 73 0.052492486450 Ilmari Vahteristo, 2026.
30 74 0.054354656515 Henry Cohn, 2026, needs more optimization.
30 75 0.056244486017 Ilmari Vahteristo, 2026.
30 76 0.057653765926 Ilmari Vahteristo, 2026.
30 77 0.059053763774 Ilmari Vahteristo, 2026.
30 78 0.060514438100 Henry Cohn, 2026, needs more optimization.
30 79 0.062144623806 Henry Cohn, 2026, needs more optimization.
30 80 0.062598541384 Henry Cohn, 2026, needs more optimization.
30 81 0.062840662877 Henry Cohn, 2026, needs more optimization.
30 82 0.064290493137 Henry Cohn, 2026, needs more optimization.
30 83 0.065116353468 Henry Cohn, 2026, needs more optimization.
30 84 0.066460260232 Henry Cohn, 2026, needs more optimization.
30 85 0.068034028230 Henry Cohn, 2026, needs more optimization.
30 86 0.069489198859 Henry Cohn, 2026, needs more optimization.
30 87 0.072159042163 Henry Cohn, 2026, needs more optimization.
30 88 0.073370448724 Henry Cohn, 2026, needs more optimization.
30 89 0.074313960235 Henry Cohn, 2026, needs more optimization.
30 90 0.074431580852 Henry Cohn, 2026, needs more optimization.
30 91 0.075429100149 Henry Cohn, 2026, needs more optimization.
30 92 0.076299924411 Henry Cohn, 2026, needs more optimization.
30 93 0.076899900336 Henry Cohn, 2026, needs more optimization.
30 94 0.076905071341 Henry Cohn, 2026, needs more optimization.
30 95 0.076937705910 Henry Cohn, 2026, needs more optimization.
30 96 0.077028880437 Henry Cohn, 2026, needs more optimization.
30 97 0.077180879266 Henry Cohn, 2026, needs more optimization.
30 98 0.077277068756 Henry Cohn, 2026, needs more optimization.
30 99 0.077386849218 Henry Cohn, 2026, needs more optimization.
30 100 0.077770984179 Henry Cohn, 2026, needs more optimization.
30 101 0.078157129479 Henry Cohn, 2026, needs more optimization.
30 102 0.078553472072 Henry Cohn, 2026, needs more optimization.
30 103 0.078825215956 Henry Cohn, 2026, needs more optimization.
30 104 0.079148122194 Henry Cohn, 2026, needs more optimization.
30 105 0.079852427106 Henry Cohn, 2026, needs more optimization.
30 106 0.080665835771 Henry Cohn, 2026, needs more optimization.
30 107 0.080684245067 Henry Cohn, 2026, needs more optimization.
30 108 0.080814373456 Henry Cohn, 2026, needs more optimization.
30 109 0.081524428663 Henry Cohn, 2026, needs more optimization.
30 110 0.082137985698 Henry Cohn, 2026, needs more optimization.
30 111 0.082309251353 Henry Cohn, 2026, needs more optimization.
30 112 0.084409892382 Henry Cohn, 2026, needs more optimization.
30 113 0.085914924219 Henry Cohn, 2026, needs more optimization.
30 114 0.086333380579 Orthogonal union of 112 points in 29 dimensions and 2 points in 1 dimension.
111⁢x2+2⁢x−1
30 115 0.088411692419 Henry Cohn, 2026, needs more optimization.
30 116 0.088510476812 Henry Cohn, 2026, needs more optimization.
30 117 0.088766957745 Henry Cohn, 2026, needs more optimization.
30 118 0.089139731587 Henry Cohn, 2026, needs more optimization.
30 119 0.089696084437 Henry Cohn, 2026, needs more optimization.
30 120 0.090074915033 Henry Cohn, 2026, needs more optimization.
30 121 0.090268240546 Henry Cohn, 2026, needs more optimization.
30 122 0.090485334921 Henry Cohn, 2026, needs more optimization.
30 123 0.090688812771 Henry Cohn, 2026, needs more optimization.
30 124 0.090790944141 Henry Cohn, 2026, needs more optimization.
30 125 0.091219578568 Henry Cohn, 2026, needs more optimization.
30 126 0.091624817213 Henry Cohn, 2026, needs more optimization.
30 127 0.092702729559 Henry Cohn, 2026, needs more optimization.
30 128 0.094163220916 Henry Cohn, 2026, needs more optimization.
30 129 0.095345362316 Henry Cohn, 2026, needs more optimization.
30 130 0.097375496169 Henry Cohn, 2026, needs more optimization.
30 131 0.098512388174 Henry Cohn, 2026, needs more optimization.
30 132 0.099549075151 Henry Cohn, 2026, needs more optimization.
30 133 0.100627373656 Henry Cohn, 2026, needs more optimization.
30 134 0.102005780801 Henry Cohn, 2026, needs more optimization.
30 135 0.102542682072 Henry Cohn, 2026, needs more optimization.
30 136 0.102554222725 Henry Cohn, 2026, needs more optimization.
30 137 0.102576170203 Henry Cohn, 2026, needs more optimization.
30 138 0.102587635511 Henry Cohn, 2026, needs more optimization.
30 139 0.102620453583 Henry Cohn, 2026, needs more optimization.
30 140 0.102946028795 Henry Cohn, 2026, needs more optimization.
30 141 0.103465733046 Henry Cohn, 2026, needs more optimization.
30 142 0.104553086218 Henry Cohn, 2026, needs more optimization.
30 143 0.105327319283 Henry Cohn, 2026, needs more optimization.
30 144 0.106168230867 Henry Cohn, 2026, needs more optimization.
30 145 0.107203617626 Henry Cohn, 2026, needs more optimization.
30 146 0.108228518729 Henry Cohn, 2026, needs more optimization.
30 147 0.108928258546 Henry Cohn, 2026, needs more optimization.
30 148 0.109291334803 Henry Cohn, 2026, needs more optimization.
30 149 0.109890878864 Henry Cohn, 2026, needs more optimization.
30 150 0.110412128587 Henry Cohn, 2026, needs more optimization.
30 151 0.110744160793 Henry Cohn, 2026, needs more optimization.
30 152 0.111404547627 Henry Cohn, 2026, needs more optimization.
30 153 0.112199756927 Henry Cohn, 2026, needs more optimization.
30 154 0.112752829909 Henry Cohn, 2026, needs more optimization.
30 155 0.113484496254 Henry Cohn, 2026, needs more optimization.
30 156 0.114169051259 Henry Cohn, 2026, needs more optimization.
30 157 0.115172511136 Henry Cohn, 2026, needs more optimization.
30 158 0.116193573730 Henry Cohn, 2026, needs more optimization.
30 159 0.117143959882 Henry Cohn, 2026, needs more optimization.
30 160 0.118118645618 Henry Cohn, 2026, needs more optimization.
30 161 0.118698421180 Henry Cohn, 2026, needs more optimization.
30 162 0.119883308300 Henry Cohn, 2026, needs more optimization.
30 163 0.120997353093 Henry Cohn, 2026, needs more optimization.
30 164 0.121560008636 Henry Cohn, 2026, needs more optimization.
30 165 0.122518921145 Henry Cohn, 2026, needs more optimization.
30 166 0.123252063669 Henry Cohn, 2026, needs more optimization.
30 167 0.124276530343 Henry Cohn, 2026, needs more optimization.
30 168 0.125310611651 Henry Cohn, 2026, needs more optimization.
30 169 0.126468094249 Henry Cohn, 2026, needs more optimization.
30 170 0.127109070005 Henry Cohn, 2026, needs more optimization.
30 171 0.127882372608 Henry Cohn, 2026, needs more optimization.
30 172 0.128775263974 Henry Cohn, 2026, needs more optimization.
30 173 0.129578905260 Henry Cohn, 2026, needs more optimization.
30 174 0.130823100959 Henry Cohn, 2026, needs more optimization.
30 175 0.132777098940 Orthogonal union of 173 points in 29 dimensions and 2 points in 1 dimension.
30 176 0.132874209547 Henry Cohn, 2026, needs more optimization.
30 177 0.133012362800 Henry Cohn, 2026, needs more optimization.
30 178 0.133121030357 Henry Cohn, 2026, needs more optimization.
30 179 0.133377487293 Henry Cohn, 2026, needs more optimization.
30 180 0.133528454411 Henry Cohn, 2026, needs more optimization.
30 181 0.133752471129 Henry Cohn, 2026, needs more optimization.
30 182 0.133804489861 Henry Cohn, 2026, needs more optimization.
30 183 0.133946181704 Henry Cohn, 2026, needs more optimization.
30 184 0.134041685342 Henry Cohn, 2026, needs more optimization.
30 185 0.134217066364 Henry Cohn, 2026, needs more optimization.
30 186 0.134474302929 Henry Cohn, 2026, needs more optimization.
30 187 0.134681179941 Henry Cohn, 2026, needs more optimization.
30 188 0.134716189334 Henry Cohn, 2026, needs more optimization.
30 189 0.135409240463 Henry Cohn, 2026, needs more optimization.
30 190 0.135833773537 Henry Cohn, 2026, needs more optimization.
30 191 0.136372124054 Henry Cohn, 2026, needs more optimization.
30 192 0.136868430776 Henry Cohn, 2026, needs more optimization.
30 193 0.137304279011 Henry Cohn, 2026, needs more optimization.
30 194 0.137792709516 Henry Cohn, 2026, needs more optimization.
30 195 0.138379181445 Henry Cohn, 2026, needs more optimization.
30 196 0.139225870116 Henry Cohn, 2026, needs more optimization.
30 197 0.140045479908 Henry Cohn, 2026, needs more optimization.
30 198 0.140366554274 Henry Cohn, 2026, needs more optimization.
30 199 0.140882871925 Henry Cohn, 2026, needs more optimization.
30 200 0.141113719092 Henry Cohn, 2026, needs more optimization.
30 201 0.141336633550 Henry Cohn, 2026, needs more optimization.
30 202 0.141395969861 Henry Cohn, 2026, needs more optimization.
30 203 0.141481329440 Henry Cohn, 2026, needs more optimization.
30 204 0.141620450570 Henry Cohn, 2026, needs more optimization.
30 205 0.141708846626 Henry Cohn, 2026, needs more optimization.
30 206 0.141885046504 Henry Cohn, 2026, needs more optimization.
30 207 0.142000349585 Henry Cohn, 2026, needs more optimization.
30 208 0.142059404912 Henry Cohn, 2026, needs more optimization.
30 209 0.142119420209 Henry Cohn, 2026, needs more optimization.
30 210 0.142197847982 Henry Cohn, 2026, needs more optimization.
30 211 0.142356770648 Henry Cohn, 2026, needs more optimization.
30 213 0.142389978941 Henry Cohn, 2026, needs more optimization.
30 214 0.142502608637 Henry Cohn, 2026, needs more optimization.
30 215 0.142651635132 Henry Cohn, 2026, needs more optimization.
30 216 0.142957097006 Henry Cohn, 2026, needs more optimization.
30 217 0.143004520707 Henry Cohn, 2026, needs more optimization.
30 218 0.143284836785 Henry Cohn, 2026, needs more optimization.
30 219 0.143742379616 Henry Cohn, 2026, needs more optimization.
30 220 0.144047234703 Henry Cohn, 2026, needs more optimization.
30 221 0.144466655682 Henry Cohn, 2026, needs more optimization.
30 222 0.145008812108 Henry Cohn, 2026, needs more optimization.
30 223 0.145801859896 Henry Cohn, 2026, needs more optimization.
30 224 0.146280431376 Henry Cohn, 2026, needs more optimization.
30 225 0.146844335619 Henry Cohn, 2026, needs more optimization.
30 226 0.146996774319 Henry Cohn, 2026, needs more optimization.
30 227 0.147574167934 Henry Cohn, 2026, needs more optimization.
30 228 0.148149208028 Henry Cohn, 2026, needs more optimization.
30 229 0.148413013290 Henry Cohn, 2026, needs more optimization.
30 230 0.148895859133 Henry Cohn, 2026, needs more optimization.
30 231 0.149162320975 Henry Cohn, 2026, needs more optimization.
30 232 0.149739099217 Henry Cohn, 2026, needs more optimization.
30 233 0.150421501271 Henry Cohn, 2026, needs more optimization.
30 234 0.150991742870 Henry Cohn, 2026, needs more optimization.
30 235 0.151407500809 Henry Cohn, 2026, needs more optimization.
30 236 0.152330292922 Henry Cohn, 2026, needs more optimization.
30 237 0.152993298295 Henry Cohn, 2026, needs more optimization.
30 238 0.153602187886 Henry Cohn, 2026, needs more optimization.
30 239 0.154785297300 Henry Cohn, 2026, needs more optimization.
30 240 0.155500278615 Henry Cohn, 2026, needs more optimization.
30 241 0.157118195123 Henry Cohn, 2026, needs more optimization.
30 242 0.157205488001 Henry Cohn, 2026, needs more optimization.
30 243 0.158063875706 Henry Cohn, 2026, needs more optimization.
30 244 0.158080682755 Henry Cohn, 2026, needs more optimization.
30 245 0.158470425414 Henry Cohn, 2026, needs more optimization.
30 246 0.159388865247 Henry Cohn, 2026, needs more optimization.
30 247 0.159414016083 Henry Cohn, 2026, needs more optimization.
30 248 0.159553983219 Henry Cohn, 2026, needs more optimization.
30 249 0.159588021349 Henry Cohn, 2026, needs more optimization.
30 250 0.160377813467 Henry Cohn, 2026, needs more optimization.
30 251 0.160405924336 Henry Cohn, 2026, needs more optimization.
30 252 0.160444386999 Henry Cohn, 2026, needs more optimization.
30 253 0.160502781721 Henry Cohn, 2026, needs more optimization.
30 254 0.160540059681 Henry Cohn, 2026, needs more optimization.
30 255 0.160572193922 Henry Cohn, 2026, needs more optimization.
30 256 0.160639810212 Henry Cohn, 2026, needs more optimization.
30 257 0.160692153013 Henry Cohn, 2026, needs more optimization.
30 258 0.160723005421 Henry Cohn, 2026, needs more optimization.
30 259 0.160756819419 Henry Cohn, 2026, needs more optimization.
30 260 0.160797767070 Henry Cohn, 2026, needs more optimization.
30 261 0.160848086319 Henry Cohn, 2026, needs more optimization.
30 262 0.160893850546 Henry Cohn, 2026, needs more optimization.
30 263 0.160937554747 Henry Cohn, 2026, needs more optimization.
30 264 0.161001270501 Henry Cohn, 2026, needs more optimization.
30 265 0.161040273593 Henry Cohn, 2026, needs more optimization.
30 266 0.161189369449 Henry Cohn, 2026, needs more optimization.
30 267 0.161584735708 Henry Cohn, 2026, needs more optimization.
30 269 0.161824282027 Henry Cohn, 2026, needs more optimization.
30 270 0.161876533651 Henry Cohn, 2026, needs more optimization.
30 275 0.161883303905 Henry Cohn, 2026, needs more optimization.
30 276 0.162018905033 Henry Cohn, 2026, needs more optimization.
30 277 0.162054776249 Henry Cohn, 2026, needs more optimization.
30 278 0.162167416964 Henry Cohn, 2026, needs more optimization.
30 279 0.162250570612 Henry Cohn, 2026, needs more optimization.
30 280 0.162614818922 Henry Cohn, 2026, needs more optimization.
30 281 0.162857310340 Henry Cohn, 2026, needs more optimization.
30 282 0.163576214200 Henry Cohn, 2026, needs more optimization.
30 283 0.164228728988 Henry Cohn, 2026, needs more optimization.
30 284 0.164475805018 Henry Cohn, 2026, needs more optimization.
30 285 0.165453112756 Henry Cohn, 2026, needs more optimization.
30 286 0.165504846353 Henry Cohn, 2026, needs more optimization.
30 287 0.165532577858 Henry Cohn, 2026, needs more optimization.
30 288 0.165600722484 Henry Cohn, 2026, needs more optimization.
30 290 0.165842479520 Henry Cohn, 2026, needs more optimization.
30 291 0.166088480470 Henry Cohn, 2026, needs more optimization.
30 292 0.166116146189 Henry Cohn, 2026, needs more optimization.
30 293 0.166144700871 Henry Cohn, 2026, needs more optimization.
30 294 0.166173272541 Henry Cohn, 2026, needs more optimization.
30 295 0.166204936677 Henry Cohn, 2026, needs more optimization.
30 296 0.166232023417 Henry Cohn, 2026, needs more optimization.
30 297 0.166260964819 Henry Cohn, 2026, needs more optimization.
30 298 0.166291501003 Henry Cohn, 2026, needs more optimization.
30 299 0.166323816581 Henry Cohn, 2026, needs more optimization.
30 300 0.166358525068 Henry Cohn, 2026, needs more optimization.
30 301 0.166485910986 Henry Cohn, 2026, needs more optimization.
30 302 0.166485911052 Henry Cohn, 2026, needs more optimization.
30 303 0.166681308189 Orthogonal union of 301 points in 29 dimensions and 2 points in 1 dimension.
30 304 0.176000456719 Henry Cohn, 2026, needs more optimization.
30 305 0.176030393809 Henry Cohn, 2026, needs more optimization.
30 306 0.176031946478 Henry Cohn, 2026, needs more optimization.
30 307 0.176046588051 Henry Cohn, 2025, needs more optimization.
30 308 0.176092780127 Henry Cohn, 2026, needs more optimization.
30 309 0.176268389777 Henry Cohn, 2026, needs more optimization.
30 310 0.176277663143 Henry Cohn, 2026, needs more optimization.
30 311 0.176287752274 Henry Cohn, 2025, needs more optimization.
30 312 0.176297427668 Henry Cohn, 2026, needs more optimization.
30 313 0.176309067334 Henry Cohn, 2025, needs more optimization.
30 314 0.176351126005 Henry Cohn, 2026, needs more optimization.
30 316 0.183091807867 Henry Cohn, 2026, needs more optimization.
30 324 0.184818717553 Henry Cohn, 2026, needs more optimization.
30 332 0.186189915578 Henry Cohn, 2026, needs more optimization.
30 340 0.187722842040 Henry Cohn, 2026, needs more optimization.
30 348 0.188810988910 Henry Cohn, 2026, needs more optimization.
30 356 0.190253570136 Henry Cohn, 2026, needs more optimization.
30 360 0.191182556614 Henry Cohn, 2026, needs more optimization.
30 364 0.191323371110 Henry Cohn, 2026, needs more optimization.
30 372 0.192481542472 Henry Cohn, 2026, needs more optimization.
30 376 0.193330704685 Henry Cohn, 2026, needs more optimization.
30 380 0.193729134592 Henry Cohn, 2026, needs more optimization.
30 384 0.194582190266 Henry Cohn, 2026, needs more optimization.
30 388 0.195546565577 Henry Cohn, 2026, needs more optimization.
30 392 0.196560028633 Henry Cohn, 2026, needs more optimization.
30 394 0.199999985028 Henry Cohn, 2026, needs more optimization.
30 576 0.2 Orthogonal union of 552 points in 23 dimensions and 24 points in 7 dimensions.
5⁢x−1
30 577 0.200040738021 Henry Cohn, 2025, needs more optimization.
30 584 0.200044686574 Henry Cohn, 2026, needs more optimization.
30 585 0.200045798599 Henry Cohn, 2025, needs more optimization.
30 586 0.200050687732 Henry Cohn, 2025, needs more optimization.
30 588 0.200053323442 Henry Cohn, 2026, needs more optimization.
30 590 0.200056685754 Henry Cohn, 2025, needs more optimization.
30 592 0.200062139434 Henry Cohn, 2026, needs more optimization.
30 593 0.233997314950 Henry Cohn, 2026, needs more optimization.
30 594 0.234094005201 Henry Cohn, 2026, needs more optimization.
30 595 0.234180864277 Henry Cohn, 2026, needs more optimization.
30 596 0.234300790850 Henry Cohn, 2026, needs more optimization.
30 597 0.234356299751 Henry Cohn, 2026, needs more optimization.
30 598 0.234512556904 Henry Cohn, 2026, needs more optimization.
30 599 0.234653514858 Henry Cohn, 2026, needs more optimization.
30 600 0.234739250135 Henry Cohn, 2026, needs more optimization.
30 601 0.234873647733 Henry Cohn, 2026, needs more optimization.
30 602 0.234935594669 Henry Cohn, 2026, needs more optimization.
30 603 0.235075102783 Henry Cohn, 2026, needs more optimization.
30 604 0.235095384311 Henry Cohn, 2026, needs more optimization.
30 605 0.235187552255 Henry Cohn, 2026, needs more optimization.
30 606 0.235882290588 Henry Cohn, 2026, needs more optimization.
30 607 0.235938658277 Henry Cohn, 2026, needs more optimization.
30 608 0.236017797427 Henry Cohn, 2026, needs more optimization.
30 609 0.236182241133 Henry Cohn, 2026, needs more optimization.
30 610 0.236250907023 Henry Cohn, 2026, needs more optimization.
30 611 0.236399171153 Henry Cohn, 2026, needs more optimization.
30 612 0.236420141706 Henry Cohn, 2026, needs more optimization.
30 613 0.236893313278 Henry Cohn, 2026, needs more optimization.
30 614 0.237068701693 Henry Cohn, 2026, needs more optimization.
30 615 0.237192508678 Henry Cohn, 2026, needs more optimization.
30 616 0.237310122973 Henry Cohn, 2026, needs more optimization.
30 617 0.237457528731 Henry Cohn, 2026, needs more optimization.
30 618 0.237479243529 Henry Cohn, 2026, needs more optimization.
30 620 0.237573706626 Henry Cohn, 2026, needs more optimization.
30 628 0.237783750452 Henry Cohn, 2026, needs more optimization.
30 632 0.237950384877 Henry Cohn, 2026, needs more optimization.
30 636 0.237957907490 Henry Cohn, 2026, needs more optimization.
30 640 0.238099964973 Henry Cohn, 2026, needs more optimization.
30 642 0.239119677104 Orthogonal union of 640 points in 29 dimensions and 2 points in 1 dimension.
30 644 0.239137654418 Henry Cohn, 2026, needs more optimization.
30 648 0.242238173228 Henry Cohn, 2026, needs more optimization.
30 652 0.242586591608 Henry Cohn, 2026, needs more optimization.
30 660 0.243317522967 Henry Cohn, 2026, needs more optimization.
30 686 0.243647721992 Henry Cohn, 2026, needs more optimization.
30 690 0.243900447540 Henry Cohn, 2026, needs more optimization.
30 694 0.244123391004 Henry Cohn, 2026, needs more optimization.
30 698 0.244352979885 Henry Cohn, 2026, needs more optimization.
30 702 0.244587787176 Henry Cohn, 2026, needs more optimization.
30 706 0.244809805380 Henry Cohn, 2026, needs more optimization.
30 710 0.245029327982 Henry Cohn, 2026, needs more optimization.
30 714 0.245257402869 Henry Cohn, 2026, needs more optimization.
30 718 0.245496848646 Henry Cohn, 2026, needs more optimization.
30 722 0.245741482676 Henry Cohn, 2026, needs more optimization.
30 726 0.245984136385 Henry Cohn, 2026, needs more optimization.
30 730 0.246224976332 Henry Cohn, 2026, needs more optimization.
30 734 0.246460819628 Henry Cohn, 2026, needs more optimization.
30 738 0.246727013986 Henry Cohn, 2026, needs more optimization.
30 742 0.246982002627 Henry Cohn, 2026, needs more optimization.
30 746 0.247228097521 Henry Cohn, 2026, needs more optimization.
30 750 0.247453914150 Henry Cohn, 2026, needs more optimization.
30 754 0.247676158018 Henry Cohn, 2026, needs more optimization.
30 758 0.247916829902 Henry Cohn, 2026, needs more optimization.
30 762 0.248159570068 Henry Cohn, 2026, needs more optimization.
30 766 0.248414035521 Henry Cohn, 2026, needs more optimization.
30 770 0.248680496960 Henry Cohn, 2026, needs more optimization.
30 774 0.248936211296 Henry Cohn, 2026, needs more optimization.
30 778 0.249169608073 Henry Cohn, 2026, needs more optimization.
30 782 0.249395954124 Henry Cohn, 2026, needs more optimization.
30 786 0.249573338940 Henry Cohn, 2026, needs more optimization.
30 790 0.249720601955 Henry Cohn, 2026, needs more optimization.
30 794 0.249839489373 Henry Cohn, 2026, needs more optimization.
30 798 0.249904407118 Henry Cohn, 2026, needs more optimization.
30 802 0.249935308767 Henry Cohn, 2026, needs more optimization.
30 804 0.249972526190 Henry Cohn, 2026, needs more optimization.
30 949 0.25 Orthogonal union of 945 points in 28 dimensions and 4 points in 2 dimensions.
4⁢x−1
30 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
31 63 0.026092422671 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
26071⁢x3−961⁢x2−31⁢x+1
31 64 0.030325216616 Henry Cohn, 2026, needs more optimization.
31 65 0.038587061312 Ilmari Vahteristo, 2026.
31 66 0.040710793741 Henry Cohn, 2026, needs more optimization.
31 67 0.043134050006 Henry Cohn, 2026, needs more optimization.
31 68 0.043324044266 Henry Cohn, 2026, needs more optimization.
31 69 0.043538634462 Henry Cohn, 2026, needs more optimization.
31 70 0.043787493775 Henry Cohn, 2026, needs more optimization.
31 71 0.044034236203 Henry Cohn, 2026, needs more optimization.
31 72 0.044583881522 Henry Cohn, 2026, needs more optimization.
31 73 0.048691227081 Henry Cohn, 2026, needs more optimization.
31 74 0.050104748821 Henry Cohn, 2026, needs more optimization.
31 75 0.051097142864 Henry Cohn, 2026, needs more optimization.
31 76 0.052578474484 Henry Cohn, 2026, needs more optimization.
31 77 0.054541789252 Ilmari Vahteristo, 2026.
31 78 0.055759550294 Henry Cohn, 2026, needs more optimization.
31 79 0.057285189631 Ilmari Vahteristo, 2026.
31 80 0.058638157280 Ilmari Vahteristo, 2026.
31 81 0.060011874851 Ilmari Vahteristo, 2026.
31 82 0.061360497543 Henry Cohn, 2026, needs more optimization.
31 83 0.061683432186 Henry Cohn, 2026, needs more optimization.
31 84 0.062652681104 Henry Cohn, 2026, needs more optimization.
31 85 0.063452446807 Henry Cohn, 2026, needs more optimization.
31 86 0.064512139059 Henry Cohn, 2026, needs more optimization.
31 87 0.065619149752 Henry Cohn, 2026, needs more optimization.
31 88 0.067223307140 Henry Cohn, 2026, needs more optimization.
31 89 0.069596930641 Henry Cohn, 2026, needs more optimization.
31 90 0.071124886555 Henry Cohn, 2026, needs more optimization.
31 91 0.072108555360 Henry Cohn, 2026, needs more optimization.
31 92 0.073158660173 Henry Cohn, 2026, needs more optimization.
31 93 0.074056359519 Henry Cohn, 2026, needs more optimization.
31 94 0.074944800167 Henry Cohn, 2026, needs more optimization.
31 95 0.075956287140 Henry Cohn, 2026, needs more optimization.
31 96 0.076046097199 Henry Cohn, 2026, needs more optimization.
31 97 0.076786198214 Henry Cohn, 2026, needs more optimization.
31 98 0.076842257028 Henry Cohn, 2026, needs more optimization.
31 99 0.076892626483 Henry Cohn, 2026, needs more optimization.
31 100 0.076928946092 Henry Cohn, 2026, needs more optimization.
31 101 0.076991739075 Henry Cohn, 2026, needs more optimization.
31 102 0.077155223458 Henry Cohn, 2026, needs more optimization.
31 103 0.077296138734 Henry Cohn, 2026, needs more optimization.
31 104 0.077401070294 Henry Cohn, 2026, needs more optimization.
31 105 0.077815147677 Henry Cohn, 2026, needs more optimization.
31 106 0.078458348224 Henry Cohn, 2026, needs more optimization.
31 107 0.078974504770 Henry Cohn, 2026, needs more optimization.
31 108 0.079523994794 Henry Cohn, 2026, needs more optimization.
31 109 0.079853122455 Henry Cohn, 2026, needs more optimization.
31 110 0.080605980952 Henry Cohn, 2026, needs more optimization.
31 111 0.080680295460 Henry Cohn, 2026, needs more optimization.
31 112 0.080739352548 Henry Cohn, 2026, needs more optimization.
31 113 0.081339754384 Henry Cohn, 2026, needs more optimization.
31 114 0.083168572832 Henry Cohn, 2026, needs more optimization.
31 115 0.083497109622 Henry Cohn, 2026, needs more optimization.
31 116 0.083558051521 Henry Cohn, 2026, needs more optimization.
31 117 0.084483653947 Henry Cohn, 2026, needs more optimization.
31 118 0.085849259562 Henry Cohn, 2026, needs more optimization.
31 119 0.087077651250 Henry Cohn, 2026, needs more optimization.
31 120 0.088095920467 Henry Cohn, 2026, needs more optimization.
31 121 0.088325096133 Henry Cohn, 2026, needs more optimization.
31 122 0.088727578361 Henry Cohn, 2026, needs more optimization.
31 123 0.089000677898 Henry Cohn, 2026, needs more optimization.
31 124 0.089206300374 Henry Cohn, 2026, needs more optimization.
31 125 0.089609400793 Henry Cohn, 2026, needs more optimization.
31 126 0.090088654192 Henry Cohn, 2026, needs more optimization.
31 127 0.090331299113 Henry Cohn, 2026, needs more optimization.
31 128 0.090621899615 Henry Cohn, 2026, needs more optimization.
31 129 0.090790299147 Henry Cohn, 2026, needs more optimization.
31 130 0.091274922067 Henry Cohn, 2026, needs more optimization.
31 131 0.092328860934 Henry Cohn, 2026, needs more optimization.
31 132 0.093190738521 Henry Cohn, 2026, needs more optimization.
31 133 0.094606477480 Henry Cohn, 2026, needs more optimization.
31 134 0.095448357853 Henry Cohn, 2026, needs more optimization.
31 135 0.096348341677 Henry Cohn, 2026, needs more optimization.
31 136 0.097760271961 Henry Cohn, 2026, needs more optimization.
31 137 0.098801227526 Henry Cohn, 2026, needs more optimization.
31 138 0.099762218841 Henry Cohn, 2026, needs more optimization.
31 139 0.100461320118 Henry Cohn, 2026, needs more optimization.
31 140 0.102422166238 Henry Cohn, 2026, needs more optimization.
31 141 0.102478843476 Henry Cohn, 2026, needs more optimization.
31 142 0.102494593718 Henry Cohn, 2026, needs more optimization.
31 143 0.102507706916 Henry Cohn, 2026, needs more optimization.
31 144 0.102565682949 Henry Cohn, 2026, needs more optimization.
31 145 0.102694774029 Henry Cohn, 2026, needs more optimization.
31 146 0.102851684934 Henry Cohn, 2026, needs more optimization.
31 147 0.103822486786 Henry Cohn, 2026, needs more optimization.
31 148 0.104757380322 Henry Cohn, 2026, needs more optimization.
31 149 0.105241075846 Henry Cohn, 2026, needs more optimization.
31 150 0.106275090447 Henry Cohn, 2026, needs more optimization.
31 151 0.107207111028 Henry Cohn, 2026, needs more optimization.
31 152 0.107984512466 Henry Cohn, 2026, needs more optimization.
31 153 0.108742896634 Henry Cohn, 2026, needs more optimization.
31 154 0.109420016442 Henry Cohn, 2026, needs more optimization.
31 155 0.109986285199 Henry Cohn, 2026, needs more optimization.
31 156 0.110202674835 Henry Cohn, 2026, needs more optimization.
31 157 0.110367715912 Henry Cohn, 2026, needs more optimization.
31 158 0.110466553846 Henry Cohn, 2026, needs more optimization.
31 159 0.110683803280 Henry Cohn, 2026, needs more optimization.
31 160 0.111217540401 Henry Cohn, 2026, needs more optimization.
31 161 0.111539507563 Henry Cohn, 2026, needs more optimization.
31 162 0.112468247005 Henry Cohn, 2026, needs more optimization.
31 163 0.113078481523 Henry Cohn, 2026, needs more optimization.
31 164 0.113823417183 Henry Cohn, 2026, needs more optimization.
31 165 0.115183868344 Henry Cohn, 2026, needs more optimization.
31 166 0.116356734148 Henry Cohn, 2026, needs more optimization.
31 167 0.117521328551 Henry Cohn, 2026, needs more optimization.
31 168 0.118819070702 Henry Cohn, 2026, needs more optimization.
31 169 0.119636177555 Henry Cohn, 2026, needs more optimization.
31 170 0.120660659360 Henry Cohn, 2026, needs more optimization.
31 171 0.121452014016 Henry Cohn, 2026, needs more optimization.
31 172 0.122119461193 Henry Cohn, 2026, needs more optimization.
31 173 0.123228235584 Henry Cohn, 2026, needs more optimization.
31 174 0.123738719612 Henry Cohn, 2026, needs more optimization.
31 175 0.124859023910 Henry Cohn, 2026, needs more optimization.
31 176 0.125859659474 Henry Cohn, 2026, needs more optimization.
31 177 0.126373665079 Henry Cohn, 2026, needs more optimization.
31 178 0.127144098776 Henry Cohn, 2026, needs more optimization.
31 179 0.127716899000 Henry Cohn, 2026, needs more optimization.
31 180 0.128401338197 Henry Cohn, 2026, needs more optimization.
31 181 0.129278763284 Henry Cohn, 2026, needs more optimization.
31 182 0.130086389341 Henry Cohn, 2026, needs more optimization.
31 183 0.132054101754 Henry Cohn, 2026, needs more optimization.
31 184 0.132152491049 Henry Cohn, 2026, needs more optimization.
31 185 0.132251312514 Henry Cohn, 2026, needs more optimization.
31 186 0.132366992761 Henry Cohn, 2026, needs more optimization.
31 187 0.132734790766 Henry Cohn, 2026, needs more optimization.
31 188 0.133016217378 Henry Cohn, 2026, needs more optimization.
31 189 0.133301400553 Henry Cohn, 2026, needs more optimization.
31 190 0.133452866610 Henry Cohn, 2026, needs more optimization.
31 191 0.133574289076 Henry Cohn, 2026, needs more optimization.
31 192 0.133858559759 Henry Cohn, 2026, needs more optimization.
31 193 0.134290158252 Henry Cohn, 2026, needs more optimization.
31 194 0.134503469748 Henry Cohn, 2026, needs more optimization.
31 195 0.134630195233 Henry Cohn, 2026, needs more optimization.
31 196 0.135099277041 Henry Cohn, 2026, needs more optimization.
31 197 0.135248404050 Henry Cohn, 2026, needs more optimization.
31 198 0.135871452250 Henry Cohn, 2026, needs more optimization.
31 199 0.136160146142 Henry Cohn, 2026, needs more optimization.
31 200 0.136646686262 Henry Cohn, 2026, needs more optimization.
31 201 0.137004779134 Henry Cohn, 2026, needs more optimization.
31 202 0.137540252130 Henry Cohn, 2026, needs more optimization.
31 203 0.138204072757 Henry Cohn, 2026, needs more optimization.
31 204 0.138810748300 Henry Cohn, 2026, needs more optimization.
31 205 0.139270214731 Henry Cohn, 2026, needs more optimization.
31 206 0.139750148388 Henry Cohn, 2026, needs more optimization.
31 207 0.140395325718 Henry Cohn, 2026, needs more optimization.
31 208 0.140643987385 Henry Cohn, 2026, needs more optimization.
31 209 0.140808022215 Henry Cohn, 2026, needs more optimization.
31 210 0.140964551496 Henry Cohn, 2026, needs more optimization.
31 211 0.141056243064 Henry Cohn, 2026, needs more optimization.
31 212 0.141100255696 Henry Cohn, 2026, needs more optimization.
31 213 0.141168642097 Henry Cohn, 2026, needs more optimization.
31 214 0.141227718907 Henry Cohn, 2026, needs more optimization.
31 215 0.141341503421 Henry Cohn, 2026, needs more optimization.
31 216 0.141424455179 Henry Cohn, 2026, needs more optimization.
31 217 0.141517022929 Henry Cohn, 2026, needs more optimization.
31 218 0.141680025848 Henry Cohn, 2026, needs more optimization.
31 219 0.141833656091 Henry Cohn, 2026, needs more optimization.
31 220 0.142079580041 Henry Cohn, 2026, needs more optimization.
31 221 0.142172465059 Henry Cohn, 2026, needs more optimization.
31 222 0.142219595795 Henry Cohn, 2026, needs more optimization.
31 223 0.142246002619 Henry Cohn, 2026, needs more optimization.
31 224 0.142582522778 Henry Cohn, 2026, needs more optimization.
31 225 0.142619823916 Henry Cohn, 2026, needs more optimization.
31 226 0.142915613598 Henry Cohn, 2026, needs more optimization.
31 227 0.143186198982 Henry Cohn, 2026, needs more optimization.
31 228 0.143459229682 Henry Cohn, 2026, needs more optimization.
31 229 0.143883563006 Henry Cohn, 2026, needs more optimization.
31 230 0.144481816454 Henry Cohn, 2026, needs more optimization.
31 231 0.145024585197 Henry Cohn, 2026, needs more optimization.
31 232 0.145457411025 Henry Cohn, 2026, needs more optimization.
31 233 0.145518998520 Henry Cohn, 2026, needs more optimization.
31 234 0.145741549562 Henry Cohn, 2026, needs more optimization.
31 235 0.146770143955 Henry Cohn, 2026, needs more optimization.
31 236 0.146903577985 Henry Cohn, 2026, needs more optimization.
31 237 0.147471709386 Henry Cohn, 2026, needs more optimization.
31 238 0.147906526072 Henry Cohn, 2026, needs more optimization.
31 239 0.148101331959 Henry Cohn, 2026, needs more optimization.
31 240 0.148334696328 Henry Cohn, 2026, needs more optimization.
31 241 0.149092877861 Henry Cohn, 2026, needs more optimization.
31 242 0.149622396772 Henry Cohn, 2026, needs more optimization.
31 243 0.150264060209 Henry Cohn, 2026, needs more optimization.
31 244 0.150420089463 Henry Cohn, 2026, needs more optimization.
31 245 0.150953103710 Henry Cohn, 2026, needs more optimization.
31 246 0.151589576334 Henry Cohn, 2026, needs more optimization.
31 247 0.152192326456 Henry Cohn, 2026, needs more optimization.
31 248 0.152567767623 Henry Cohn, 2026, needs more optimization.
31 249 0.153504426690 Henry Cohn, 2026, needs more optimization.
31 250 0.153840919150 Henry Cohn, 2026, needs more optimization.
31 251 0.154500352140 Henry Cohn, 2026, needs more optimization.
31 252 0.155286936280 Henry Cohn, 2026, needs more optimization.
31 253 0.155986010319 Henry Cohn, 2026, needs more optimization.
31 254 0.156811259300 Henry Cohn, 2026, needs more optimization.
31 255 0.157859032643 Henry Cohn, 2026, needs more optimization.
31 256 0.157893617471 Henry Cohn, 2026, needs more optimization.
31 257 0.158031001765 Henry Cohn, 2026, needs more optimization.
31 258 0.158516840684 Henry Cohn, 2026, needs more optimization.
31 259 0.159130652171 Henry Cohn, 2026, needs more optimization.
31 260 0.159185321778 Henry Cohn, 2026, needs more optimization.
31 261 0.159221104627 Henry Cohn, 2026, needs more optimization.
31 262 0.159391453077 Henry Cohn, 2026, needs more optimization.
31 263 0.159621335916 Henry Cohn, 2026, needs more optimization.
31 264 0.159650739370 Henry Cohn, 2026, needs more optimization.
31 265 0.160021313587 Henry Cohn, 2026, needs more optimization.
31 266 0.160053592860 Henry Cohn, 2026, needs more optimization.
31 267 0.160073154171 Henry Cohn, 2026, needs more optimization.
31 268 0.160222359434 Henry Cohn, 2026, needs more optimization.
31 269 0.160304290854 Henry Cohn, 2026, needs more optimization.
31 270 0.160465724849 Henry Cohn, 2026, needs more optimization.
31 271 0.160489524533 Henry Cohn, 2026, needs more optimization.
31 273 0.160744220262 Henry Cohn, 2026, needs more optimization.
31 275 0.160812108817 Henry Cohn, 2026, needs more optimization.
31 276 0.160912514185 Henry Cohn, 2026, needs more optimization.
31 277 0.161369698303 Henry Cohn, 2026, needs more optimization.
31 279 0.161617401726 Henry Cohn, 2026, needs more optimization.
31 280 0.161751654446 Henry Cohn, 2026, needs more optimization.
31 281 0.161776453708 Henry Cohn, 2026, needs more optimization.
31 282 0.161900062649 Henry Cohn, 2026, needs more optimization.
31 283 0.162253339043 Henry Cohn, 2026, needs more optimization.
31 284 0.162510336015 Henry Cohn, 2026, needs more optimization.
31 285 0.162689770843 Henry Cohn, 2026, needs more optimization.
31 287 0.162808782868 Henry Cohn, 2026, needs more optimization.
31 288 0.162959910319 Henry Cohn, 2026, needs more optimization.
31 289 0.163102051289 Henry Cohn, 2026, needs more optimization.
31 290 0.163285089227 Henry Cohn, 2026, needs more optimization.
31 291 0.163484849641 Henry Cohn, 2026, needs more optimization.
31 292 0.163689188427 Henry Cohn, 2026, needs more optimization.
31 293 0.164255614696 Henry Cohn, 2026, needs more optimization.
31 294 0.164282708990 Henry Cohn, 2026, needs more optimization.
31 295 0.164351486385 Henry Cohn, 2026, needs more optimization.
31 296 0.164380156732 Henry Cohn, 2026, needs more optimization.
31 298 0.164813264665 Henry Cohn, 2026, needs more optimization.
31 300 0.165039835614 Henry Cohn, 2026, needs more optimization.
31 301 0.165517859067 Henry Cohn, 2026, needs more optimization.
31 302 0.165531195303 Henry Cohn, 2026, needs more optimization.
31 304 0.165552292076 Henry Cohn, 2026, needs more optimization.
31 305 0.165585981557 Henry Cohn, 2026, needs more optimization.
31 306 0.165596606663 Henry Cohn, 2025, needs more optimization.
31 307 0.166666666662 Henry Cohn, 2025, needs more optimization.
31 308 0.174500504398 Henry Cohn, 2026, needs more optimization.
31 309 0.174563450677 Henry Cohn, 2026, needs more optimization.
31 310 0.174573881109 Henry Cohn, 2025, needs more optimization.
31 311 0.174614374028 Henry Cohn, 2025, needs more optimization.
31 312 0.174619345986 Henry Cohn, 2026, needs more optimization.
31 313 0.175586810624 Henry Cohn, 2025, needs more optimization.
31 314 0.175643175584 Henry Cohn, 2026, needs more optimization.
31 315 0.175683376665 Henry Cohn, 2025, needs more optimization.
31 316 0.175728673343 Henry Cohn, 2026, needs more optimization.
31 317 0.175792168087 Henry Cohn, 2026, needs more optimization.
31 320 0.175814222432 Henry Cohn, 2026, needs more optimization.
31 321 0.175847644698 Henry Cohn, 2025, needs more optimization.
31 322 0.175900408725 Henry Cohn, 2025, needs more optimization.
31 323 0.176086193436 Henry Cohn, 2026, needs more optimization.
31 324 0.177577953347 Henry Cohn, 2026, needs more optimization.
31 332 0.179417147936 Henry Cohn, 2026, needs more optimization.
31 340 0.181589774872 Henry Cohn, 2026, needs more optimization.
31 348 0.183048537949 Henry Cohn, 2026, needs more optimization.
31 356 0.184750054759 Henry Cohn, 2026, needs more optimization.
31 360 0.185818398040 Henry Cohn, 2026, needs more optimization.
31 364 0.185933879747 Henry Cohn, 2026, needs more optimization.
31 372 0.187274493394 Henry Cohn, 2026, needs more optimization.
31 376 0.188304886743 Henry Cohn, 2026, needs more optimization.
31 380 0.188790386609 Henry Cohn, 2026, needs more optimization.
31 384 0.190040337084 Henry Cohn, 2026, needs more optimization.
31 388 0.193409326176 Henry Cohn, 2026, needs more optimization.
31 392 0.195292487253 Henry Cohn, 2026, needs more optimization.
31 394 0.196560028633 Orthogonal union of 392 points in 30 dimensions and 2 points in 1 dimension.
31 396 0.199851620442 Henry Cohn, 2026, needs more optimization.
31 404 0.199945716351 Henry Cohn, 2026, needs more optimization.
31 408 0.199991473197 Henry Cohn, 2026, needs more optimization.
31 410 0.199999999977 Henry Cohn, 2026, needs more optimization.
31 581 0.2 Orthogonal union of 552 points in 23 dimensions and 29 points in 8 dimensions.
5⁢x−1
31 592 0.200038666970 Henry Cohn, 2026, needs more optimization.
31 596 0.200046007219 Henry Cohn, 2026, needs more optimization.
31 598 0.200057421527 Henry Cohn, 2025, needs more optimization.
31 599 0.200078681940 Henry Cohn, 2025, needs more optimization.
31 600 0.200177422653 Henry Cohn, 2026, needs more optimization.
31 601 0.228288343916 Henry Cohn, 2025, needs more optimization.
31 602 0.228318554413 Henry Cohn, 2025, needs more optimization.
31 604 0.228521110265 Henry Cohn, 2026, needs more optimization.
31 605 0.228594247973 Henry Cohn, 2025, needs more optimization.
31 606 0.228797549321 Henry Cohn, 2025, needs more optimization.
31 608 0.228807807756 Henry Cohn, 2026, needs more optimization.
31 609 0.228911380982 Henry Cohn, 2025, needs more optimization.
31 610 0.229347513462 Henry Cohn, 2025, needs more optimization.
31 611 0.229375267707 Henry Cohn, 2025, needs more optimization.
31 612 0.229408600685 Henry Cohn, 2026, needs more optimization.
31 613 0.229611317157 Henry Cohn, 2025, needs more optimization.
31 614 0.229627532985 Henry Cohn, 2025, needs more optimization.
31 615 0.229637706316 Henry Cohn, 2025, needs more optimization.
31 616 0.229765500078 Henry Cohn, 2026, needs more optimization.
31 617 0.230100153601 Henry Cohn, 2025, needs more optimization.
31 618 0.230165831539 Henry Cohn, 2025, needs more optimization.
31 619 0.230176280206 Henry Cohn, 2025, needs more optimization.
31 620 0.230177109186 Henry Cohn, 2026, needs more optimization.
31 621 0.230213927702 Henry Cohn, 2025, needs more optimization.
31 622 0.230237270975 Henry Cohn, 2025, needs more optimization.
31 623 0.230310598199 Henry Cohn, 2025, needs more optimization.
31 624 0.230379363849 Henry Cohn, 2026, needs more optimization.
31 625 0.230419067002 Henry Cohn, 2025, needs more optimization.
31 626 0.230439769568 Henry Cohn, 2025, needs more optimization.
31 627 0.231094852576 Henry Cohn, 2025, needs more optimization.
31 628 0.231147817128 Henry Cohn, 2026, needs more optimization.
31 629 0.231170931136 Henry Cohn, 2025, needs more optimization.
31 630 0.231210954166 Henry Cohn, 2025, needs more optimization.
31 631 0.231259889127 Henry Cohn, 2025, needs more optimization.
31 632 0.231270213175 Henry Cohn, 2026, needs more optimization.
31 633 0.231302105729 Henry Cohn, 2025, needs more optimization.
31 634 0.231312934261 Henry Cohn, 2025, needs more optimization.
31 635 0.231355294469 Henry Cohn, 2025, needs more optimization.
31 636 0.231359517734 Henry Cohn, 2026, needs more optimization.
31 637 0.231392613489 Henry Cohn, 2025, needs more optimization.
31 638 0.231764210234 Henry Cohn, 2026, needs more optimization.
31 639 0.231777922428 Henry Cohn, 2026, needs more optimization.
31 640 0.231779603130 Henry Cohn, 2026, needs more optimization.
31 641 0.231798724736 Henry Cohn, 2025, needs more optimization.
31 642 0.231822795370 Henry Cohn, 2025, needs more optimization.
31 643 0.231868141337 Henry Cohn, 2025, needs more optimization.
31 644 0.231889970832 Henry Cohn, 2026, needs more optimization.
31 645 0.231933887254 Henry Cohn, 2025, needs more optimization.
31 646 0.231975442250 Henry Cohn, 2025, needs more optimization.
31 647 0.232596876139 Henry Cohn, 2025, needs more optimization.
31 648 0.232609206426 Henry Cohn, 2026, needs more optimization.
31 649 0.232626690337 Henry Cohn, 2025, needs more optimization.
31 650 0.232920515026 Henry Cohn, 2026, needs more optimization.
31 652 0.232965589233 Henry Cohn, 2026, needs more optimization.
31 653 0.232993455442 Henry Cohn, 2025, needs more optimization.
31 654 0.233006135516 Henry Cohn, 2025, needs more optimization.
31 655 0.233010397609 Henry Cohn, 2025, needs more optimization.
31 656 0.233064513885 Henry Cohn, 2026, needs more optimization.
31 657 0.233084750151 Henry Cohn, 2025, needs more optimization.
31 658 0.233159875790 Henry Cohn, 2025, needs more optimization.
31 659 0.233246714387 Henry Cohn, 2025, needs more optimization.
31 660 0.233280732911 Henry Cohn, 2026, needs more optimization.
31 662 0.233306780230 Henry Cohn, 2025, needs more optimization.
31 663 0.233377399103 Henry Cohn, 2025, needs more optimization.
31 664 0.233396415455 Henry Cohn, 2026, needs more optimization.
31 665 0.233439114500 Henry Cohn, 2025, needs more optimization.
31 666 0.233459192577 Henry Cohn, 2025, needs more optimization.
31 667 0.233485716668 Henry Cohn, 2025, needs more optimization.
31 668 0.233495305468 Henry Cohn, 2026, needs more optimization.
31 669 0.233531137768 Henry Cohn, 2025, needs more optimization.
31 670 0.234106079119 Henry Cohn, 2025, needs more optimization.
31 672 0.234148576014 Henry Cohn, 2026, needs more optimization.
31 673 0.234264037303 Henry Cohn, 2025, needs more optimization.
31 674 0.234286780563 Henry Cohn, 2025, needs more optimization.
31 675 0.234316213878 Henry Cohn, 2025, needs more optimization.
31 676 0.234354210179 Henry Cohn, 2026, needs more optimization.
31 677 0.234754103881 Henry Cohn, 2025, needs more optimization.
31 678 0.234776072945 Henry Cohn, 2025, needs more optimization.
31 679 0.234784015578 Henry Cohn, 2025, needs more optimization.
31 680 0.234808509908 Henry Cohn, 2026, needs more optimization.
31 681 0.234853838763 Henry Cohn, 2025, needs more optimization.
31 682 0.235210375825 Henry Cohn, 2025, needs more optimization.
31 684 0.235219164902 Henry Cohn, 2026, needs more optimization.
31 685 0.235307691937 Henry Cohn, 2025, needs more optimization.
31 686 0.235358812009 Henry Cohn, 2026, needs more optimization.
31 687 0.235389063723 Henry Cohn, 2025, needs more optimization.
31 688 0.235470730772 Henry Cohn, 2026, needs more optimization.
31 689 0.235595152506 Henry Cohn, 2025, needs more optimization.
31 690 0.235628701464 Henry Cohn, 2026, needs more optimization.
31 691 0.235707236567 Henry Cohn, 2025, needs more optimization.
31 692 0.235994166840 Henry Cohn, 2026, needs more optimization.
31 694 0.236018318384 Henry Cohn, 2026, needs more optimization.
31 696 0.236057179564 Henry Cohn, 2026, needs more optimization.
31 697 0.236090388931 Henry Cohn, 2025, needs more optimization.
31 698 0.236108711093 Henry Cohn, 2026, needs more optimization.
31 699 0.236337835127 Henry Cohn, 2025, needs more optimization.
31 700 0.236372883806 Henry Cohn, 2026, needs more optimization.
31 701 0.236620154373 Henry Cohn, 2025, needs more optimization.
31 702 0.236622538472 Henry Cohn, 2026, needs more optimization.
31 704 0.236666774311 Henry Cohn, 2026, needs more optimization.
31 706 0.236794697892 Henry Cohn, 2026, needs more optimization.
31 707 0.236812809389 Henry Cohn, 2025, needs more optimization.
31 708 0.236966553041 Henry Cohn, 2026, needs more optimization.
31 709 0.237028687220 Henry Cohn, 2025, needs more optimization.
31 710 0.237177009598 Henry Cohn, 2026, needs more optimization.
31 711 0.237416168837 Henry Cohn, 2025, needs more optimization.
31 712 0.237459750641 Henry Cohn, 2026, needs more optimization.
31 713 0.237544942961 Henry Cohn, 2025, needs more optimization.
31 714 0.237567112353 Henry Cohn, 2026, needs more optimization.
31 716 0.237804186749 Henry Cohn, 2026, needs more optimization.
31 717 0.237933018131 Henry Cohn, 2025, needs more optimization.
31 1024 0.238095238096 Henry Cohn, 2026.
21⁢x−5
32 65 0.025347196752 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
28800⁢x3−1024⁢x2−32⁢x+1
32 66 0.029441166533 Henry Cohn, 2026, needs more optimization.
32 67 0.037511986969 Ilmari Vahteristo, 2026.
32 68 0.039710724854 Henry Cohn, 2026, needs more optimization.
32 69 0.042615993445 Henry Cohn, 2026, needs more optimization.
32 70 0.042762186512 Henry Cohn, 2026, needs more optimization.
32 71 0.043042345599 Henry Cohn, 2026, needs more optimization.
32 72 0.043340506643 Henry Cohn, 2026, needs more optimization.
32 73 0.043649527764 Henry Cohn, 2026, needs more optimization.
32 74 0.044447962656 Henry Cohn, 2026, needs more optimization.
32 75 0.047693641178 Ilmari Vahteristo, 2026.
32 76 0.049042197562 Henry Cohn, 2026, needs more optimization.
32 77 0.049882438099 Henry Cohn, 2026, needs more optimization.
32 78 0.051414892527 Henry Cohn, 2026, needs more optimization.
32 79 0.053168362134 Ilmari Vahteristo, 2026.
32 80 0.054904010753 Henry Cohn, 2026, needs more optimization.
32 81 0.056184098050 Henry Cohn, 2026, needs more optimization.
32 82 0.057036889730 Henry Cohn, 2026, needs more optimization.
32 83 0.058506443726 Henry Cohn, 2026, needs more optimization.
32 84 0.059657784537 Henry Cohn, 2026, needs more optimization.
32 85 0.060925712145 Henry Cohn, 2026, needs more optimization.
32 86 0.062006479142 Henry Cohn, 2026, needs more optimization.
32 87 0.063247297129 Henry Cohn, 2026, needs more optimization.
32 88 0.064359806873 Henry Cohn, 2026, needs more optimization.
32 89 0.065582106280 Henry Cohn, 2026, needs more optimization.
32 90 0.066424862472 Henry Cohn, 2026, needs more optimization.
32 91 0.067776836715 Henry Cohn, 2026, needs more optimization.
32 92 0.068708894977 Henry Cohn, 2026, needs more optimization.
32 93 0.069830640093 Henry Cohn, 2026, needs more optimization.
32 94 0.070659157354 Henry Cohn, 2026, needs more optimization.
32 95 0.071733246220 Henry Cohn, 2026, needs more optimization.
32 96 0.072886351659 Henry Cohn, 2026, needs more optimization.
32 97 0.073916719985 Henry Cohn, 2026, needs more optimization.
32 98 0.074757551365 Henry Cohn, 2026, needs more optimization.
32 99 0.075637353813 Henry Cohn, 2026, needs more optimization.
32 100 0.075727405672 Henry Cohn, 2026, needs more optimization.
32 101 0.075940928453 Henry Cohn, 2026, needs more optimization.
32 102 0.076409096042 Henry Cohn, 2026, needs more optimization.
32 103 0.076810158552 Henry Cohn, 2026, needs more optimization.
32 104 0.076963644534 Henry Cohn, 2026, needs more optimization.
32 105 0.077085292560 Henry Cohn, 2026, needs more optimization.
32 106 0.077299840277 Henry Cohn, 2026, needs more optimization.
32 107 0.077429840087 Henry Cohn, 2026, needs more optimization.
32 108 0.077645975216 Henry Cohn, 2026, needs more optimization.
32 109 0.077922450683 Henry Cohn, 2026, needs more optimization.
32 110 0.078063116607 Henry Cohn, 2026, needs more optimization.
32 111 0.078890320737 Henry Cohn, 2026, needs more optimization.
32 112 0.079747136650 Henry Cohn, 2026, needs more optimization.
32 113 0.079895122413 Henry Cohn, 2026, needs more optimization.
32 114 0.080608480804 Henry Cohn, 2026, needs more optimization.
32 115 0.080644771190 Henry Cohn, 2026, needs more optimization.
32 116 0.080914992274 Henry Cohn, 2026, needs more optimization.
32 117 0.081383865655 Henry Cohn, 2026, needs more optimization.
32 118 0.081659658803 Henry Cohn, 2026, needs more optimization.
32 119 0.082503185606 Henry Cohn, 2026, needs more optimization.
32 120 0.083465320166 Henry Cohn, 2026, needs more optimization.
32 121 0.084554139069 Henry Cohn, 2026, needs more optimization.
32 122 0.085358072105 Henry Cohn, 2026, needs more optimization.
32 123 0.086591334324 Henry Cohn, 2026, needs more optimization.
32 124 0.087059505546 Henry Cohn, 2026, needs more optimization.
32 125 0.088023910803 Henry Cohn, 2026, needs more optimization.
32 126 0.088509446766 Henry Cohn, 2026, needs more optimization.
32 127 0.088536804223 Henry Cohn, 2026, needs more optimization.
32 128 0.089085099234 Henry Cohn, 2026, needs more optimization.
32 129 0.089432017581 Henry Cohn, 2026, needs more optimization.
32 130 0.089871690460 Henry Cohn, 2026, needs more optimization.
32 131 0.090113696411 Henry Cohn, 2026, needs more optimization.
32 132 0.090249107937 Henry Cohn, 2026, needs more optimization.
32 133 0.090281178993 Henry Cohn, 2026, needs more optimization.
32 134 0.090331367551 Henry Cohn, 2026, needs more optimization.
32 135 0.090335531945 Henry Cohn, 2026, needs more optimization.
32 136 0.091215456999 Henry Cohn, 2026, needs more optimization.
32 137 0.092453230968 Henry Cohn, 2026, needs more optimization.
32 138 0.093412347488 Henry Cohn, 2026, needs more optimization.
32 139 0.095158706422 Henry Cohn, 2026, needs more optimization.
32 140 0.096368188780 Henry Cohn, 2026, needs more optimization.
32 141 0.098215151995 Henry Cohn, 2026, needs more optimization.
32 142 0.098250816737 Henry Cohn, 2026, needs more optimization.
32 143 0.099384114371 Henry Cohn, 2026, needs more optimization.
32 144 0.100184845981 Henry Cohn, 2026, needs more optimization.
32 145 0.100888080487 Henry Cohn, 2026, needs more optimization.
32 148 0.102463139198 Henry Cohn, 2026, needs more optimization.
32 149 0.102569501981 Henry Cohn, 2026, needs more optimization.
32 150 0.102698434698 Henry Cohn, 2026, needs more optimization.
32 151 0.102833969844 Henry Cohn, 2026, needs more optimization.
32 152 0.103232223823 Henry Cohn, 2026, needs more optimization.
32 153 0.103930302971 Henry Cohn, 2026, needs more optimization.
32 154 0.104751924739 Henry Cohn, 2026, needs more optimization.
32 155 0.105320845206 Henry Cohn, 2026, needs more optimization.
32 156 0.105926665934 Henry Cohn, 2026, needs more optimization.
32 157 0.106533005256 Henry Cohn, 2026, needs more optimization.
32 158 0.107102606713 Henry Cohn, 2026, needs more optimization.
32 159 0.107330372182 Henry Cohn, 2026, needs more optimization.
32 160 0.108096610129 Henry Cohn, 2026, needs more optimization.
32 161 0.108291145375 Henry Cohn, 2026, needs more optimization.
32 162 0.108676291751 Henry Cohn, 2026, needs more optimization.
32 163 0.109377596864 Henry Cohn, 2026, needs more optimization.
32 164 0.109560375463 Henry Cohn, 2026, needs more optimization.
32 165 0.110273717526 Henry Cohn, 2026, needs more optimization.
32 166 0.110700364502 Henry Cohn, 2026, needs more optimization.
32 167 0.112584932175 Henry Cohn, 2026, needs more optimization.
32 168 0.113712165297 Henry Cohn, 2026, needs more optimization.
32 169 0.113857641809 Henry Cohn, 2026, needs more optimization.
32 170 0.114657446013 Henry Cohn, 2026, needs more optimization.
32 171 0.115132066646 Henry Cohn, 2026, needs more optimization.
32 172 0.115878254470 Henry Cohn, 2026, needs more optimization.
32 173 0.116724300057 Henry Cohn, 2026, needs more optimization.
32 174 0.117640985490 Henry Cohn, 2026, needs more optimization.
32 175 0.118384750521 Henry Cohn, 2026, needs more optimization.
32 176 0.119041787347 Henry Cohn, 2026, needs more optimization.
32 177 0.119617392519 Henry Cohn, 2026, needs more optimization.
32 178 0.120441667620 Henry Cohn, 2026, needs more optimization.
32 179 0.121560515259 Henry Cohn, 2026, needs more optimization.
32 180 0.122124670613 Henry Cohn, 2026, needs more optimization.
32 181 0.122767126691 Henry Cohn, 2026, needs more optimization.
32 182 0.123551304414 Henry Cohn, 2026, needs more optimization.
32 183 0.124253895646 Henry Cohn, 2026, needs more optimization.
32 184 0.125040543994 Henry Cohn, 2026, needs more optimization.
32 185 0.125782789807 Henry Cohn, 2026, needs more optimization.
32 186 0.126249721557 Henry Cohn, 2026, needs more optimization.
32 187 0.126997987576 Henry Cohn, 2026, needs more optimization.
32 188 0.127685218313 Henry Cohn, 2026, needs more optimization.
32 189 0.129958754749 Henry Cohn, 2026, needs more optimization.
32 190 0.130737694404 Henry Cohn, 2026, needs more optimization.
32 191 0.131498402453 Henry Cohn, 2026, needs more optimization.
32 192 0.132150783633 Henry Cohn, 2026, needs more optimization.
32 193 0.132804137763 Henry Cohn, 2026, needs more optimization.
32 198 0.132966403408 Henry Cohn, 2026, needs more optimization.
32 199 0.133020892123 Henry Cohn, 2026, needs more optimization.
32 200 0.133114825337 Henry Cohn, 2026, needs more optimization.
32 201 0.133351219828 Henry Cohn, 2026, needs more optimization.
32 202 0.133751067644 Henry Cohn, 2026, needs more optimization.
32 203 0.133941395522 Henry Cohn, 2026, needs more optimization.
32 204 0.134301942710 Henry Cohn, 2026, needs more optimization.
32 205 0.134860972592 Henry Cohn, 2026, needs more optimization.
32 206 0.135373295293 Henry Cohn, 2026, needs more optimization.
32 207 0.135867492953 Henry Cohn, 2026, needs more optimization.
32 208 0.136154720271 Henry Cohn, 2026, needs more optimization.
32 209 0.136551269701 Henry Cohn, 2026, needs more optimization.
32 210 0.136899614983 Henry Cohn, 2026, needs more optimization.
32 211 0.137352771254 Henry Cohn, 2026, needs more optimization.
32 212 0.137822124684 Henry Cohn, 2026, needs more optimization.
32 213 0.138215030630 Henry Cohn, 2026, needs more optimization.
32 214 0.138875250651 Henry Cohn, 2026, needs more optimization.
32 215 0.139267460079 Henry Cohn, 2026, needs more optimization.
32 216 0.139765874713 Henry Cohn, 2026, needs more optimization.
32 217 0.139976430746 Henry Cohn, 2026, needs more optimization.
32 218 0.140087866143 Henry Cohn, 2026, needs more optimization.
32 219 0.140287215104 Henry Cohn, 2026, needs more optimization.
32 220 0.140351481746 Henry Cohn, 2026, needs more optimization.
32 221 0.140484401003 Henry Cohn, 2026, needs more optimization.
32 222 0.140853512036 Henry Cohn, 2026, needs more optimization.
32 223 0.140906190294 Henry Cohn, 2026, needs more optimization.
32 224 0.141126608431 Henry Cohn, 2026, needs more optimization.
32 225 0.141170435817 Henry Cohn, 2026, needs more optimization.
32 226 0.141218279206 Henry Cohn, 2026, needs more optimization.
32 227 0.141405363108 Henry Cohn, 2026, needs more optimization.
32 228 0.141467563656 Henry Cohn, 2026, needs more optimization.
32 229 0.141729421940 Henry Cohn, 2026, needs more optimization.
32 230 0.141778208443 Henry Cohn, 2026, needs more optimization.
32 231 0.141985935780 Henry Cohn, 2026, needs more optimization.
32 232 0.142031468860 Henry Cohn, 2026, needs more optimization.
32 233 0.142234908303 Henry Cohn, 2026, needs more optimization.
32 234 0.142298201777 Henry Cohn, 2026, needs more optimization.
32 235 0.142706910170 Henry Cohn, 2026, needs more optimization.
32 236 0.142799479270 Henry Cohn, 2026, needs more optimization.
32 237 0.143254975904 Henry Cohn, 2026, needs more optimization.
32 238 0.143288451497 Henry Cohn, 2026, needs more optimization.
32 239 0.143546280929 Henry Cohn, 2026, needs more optimization.
32 240 0.143682750184 Henry Cohn, 2026, needs more optimization.
32 241 0.144412996352 Henry Cohn, 2026, needs more optimization.
32 242 0.144495231547 Henry Cohn, 2026, needs more optimization.
32 243 0.145011846257 Henry Cohn, 2026, needs more optimization.
32 244 0.145317719576 Henry Cohn, 2026, needs more optimization.
32 245 0.145968752156 Henry Cohn, 2026, needs more optimization.
32 246 0.146394476252 Henry Cohn, 2026, needs more optimization.
32 247 0.146948804243 Henry Cohn, 2026, needs more optimization.
32 248 0.147194177848 Henry Cohn, 2026, needs more optimization.
32 249 0.147618508555 Henry Cohn, 2026, needs more optimization.
32 250 0.147874240625 Henry Cohn, 2026, needs more optimization.
32 251 0.148125015404 Henry Cohn, 2026, needs more optimization.
32 252 0.148668257398 Henry Cohn, 2026, needs more optimization.
32 253 0.149115961279 Henry Cohn, 2026, needs more optimization.
32 254 0.153931948493 Henry Cohn, 2026, needs more optimization.
32 255 0.154570611809 Henry Cohn, 2026, needs more optimization.
32 256 0.154848347265 Henry Cohn, 2026, needs more optimization.
32 257 0.155398175254 Henry Cohn, 2026, needs more optimization.
32 258 0.155793527495 Henry Cohn, 2026, needs more optimization.
32 259 0.155895929509 Henry Cohn, 2026, needs more optimization.
32 260 0.155925072075 Henry Cohn, 2026, needs more optimization.
32 261 0.156040265128 Henry Cohn, 2026, needs more optimization.
32 262 0.156149528233 Henry Cohn, 2026, needs more optimization.
32 263 0.156844347509 Henry Cohn, 2026, needs more optimization.
32 264 0.157037828748 Henry Cohn, 2026, needs more optimization.
32 265 0.157061777600 Henry Cohn, 2026, needs more optimization.
32 266 0.157201019839 Henry Cohn, 2026, needs more optimization.
32 267 0.157304500500 Henry Cohn, 2026, needs more optimization.
32 268 0.157423951931 Henry Cohn, 2026, needs more optimization.
32 269 0.157520327944 Henry Cohn, 2026, needs more optimization.
32 270 0.157723977759 Henry Cohn, 2026, needs more optimization.
32 271 0.158034103874 Henry Cohn, 2026, needs more optimization.
32 272 0.158143268792 Henry Cohn, 2026, needs more optimization.
32 273 0.158201032346 Henry Cohn, 2026, needs more optimization.
32 274 0.158343474308 Henry Cohn, 2026, needs more optimization.
32 275 0.158393711085 Henry Cohn, 2026, needs more optimization.
32 276 0.158444939660 Henry Cohn, 2026, needs more optimization.
32 277 0.158615633031 Henry Cohn, 2026, needs more optimization.
32 278 0.158747796273 Henry Cohn, 2026, needs more optimization.
32 279 0.159067937460 Henry Cohn, 2026, needs more optimization.
32 280 0.159138993041 Henry Cohn, 2026, needs more optimization.
32 281 0.159192599456 Henry Cohn, 2026, needs more optimization.
32 282 0.159435258038 Henry Cohn, 2026, needs more optimization.
32 283 0.159541905009 Henry Cohn, 2026, needs more optimization.
32 284 0.159840048372 Henry Cohn, 2026, needs more optimization.
32 285 0.159991985756 Henry Cohn, 2026, needs more optimization.
32 286 0.160104753370 Henry Cohn, 2026, needs more optimization.
32 287 0.160121138283 Henry Cohn, 2026, needs more optimization.
32 288 0.160320565411 Henry Cohn, 2026, needs more optimization.
32 289 0.160593115489 Henry Cohn, 2026, needs more optimization.
32 290 0.160950239548 Henry Cohn, 2026, needs more optimization.
32 291 0.160974336016 Henry Cohn, 2026, needs more optimization.
32 292 0.161155814452 Henry Cohn, 2026, needs more optimization.
32 293 0.161322140717 Henry Cohn, 2026, needs more optimization.
32 294 0.161388184705 Henry Cohn, 2026, needs more optimization.
32 295 0.161542000228 Henry Cohn, 2026, needs more optimization.
32 296 0.161699497204 Henry Cohn, 2026, needs more optimization.
32 297 0.162107072982 Henry Cohn, 2026, needs more optimization.
32 298 0.162273105492 Henry Cohn, 2026, needs more optimization.
32 299 0.162356027665 Henry Cohn, 2026, needs more optimization.
32 300 0.162519044522 Henry Cohn, 2026, needs more optimization.
32 301 0.163163113811 Henry Cohn, 2025, needs more optimization.
32 302 0.163517519625 Henry Cohn, 2025, needs more optimization.
32 303 0.163608940714 Henry Cohn, 2025, needs more optimization.
32 304 0.164101020235 Henry Cohn, 2026, needs more optimization.
32 305 0.164217939271 Henry Cohn, 2026, needs more optimization.
32 306 0.164234344669 Henry Cohn, 2026, needs more optimization.
32 307 0.164251856881 Henry Cohn, 2025, needs more optimization.
32 308 0.164285835602 Henry Cohn, 2026, needs more optimization.
32 309 0.164516330830 Henry Cohn, 2025, needs more optimization.
32 310 0.164533585225 Henry Cohn, 2025, needs more optimization.
32 311 0.164665715925 Henry Cohn, 2025, needs more optimization.
32 312 0.164736038826 Henry Cohn, 2026, needs more optimization.
32 313 0.164800531621 Henry Cohn, 2026, needs more optimization.
32 314 0.164800531709 Henry Cohn, 2025, needs more optimization.
32 315 0.164812333655 Henry Cohn, 2025, needs more optimization.
32 316 0.166683275368 Henry Cohn, 2026, needs more optimization.
32 320 0.166820612586 Henry Cohn, 2026, needs more optimization.
32 324 0.167128256291 Henry Cohn, 2026, needs more optimization.
32 332 0.167862055425 Henry Cohn, 2026, needs more optimization.
32 340 0.169122734794 Henry Cohn, 2026, needs more optimization.
32 344 0.170713548028 Henry Cohn, 2026, needs more optimization.
32 348 0.171301086515 Henry Cohn, 2026, needs more optimization.
32 352 0.172985497766 Henry Cohn, 2026, needs more optimization.
32 356 0.173388183642 Henry Cohn, 2026, needs more optimization.
32 357 0.177208538829 Henry Cohn, 2026, needs more optimization.
32 358 0.177232516751 Henry Cohn, 2025, needs more optimization.
32 360 0.177294100324 Henry Cohn, 2026, needs more optimization.
32 362 0.177336700360 Henry Cohn, 2025, needs more optimization.
32 363 0.177355864571 Henry Cohn, 2025, needs more optimization.
32 364 0.177398869824 Henry Cohn, 2026, needs more optimization.
32 365 0.177403896667 Henry Cohn, 2025, needs more optimization.
32 366 0.177457583407 Henry Cohn, 2025, needs more optimization.
32 367 0.177668635338 Henry Cohn, 2026, needs more optimization.
32 368 0.177952192805 Henry Cohn, 2026, needs more optimization.
32 369 0.177979746530 Henry Cohn, 2025, needs more optimization.
32 370 0.178032418622 Henry Cohn, 2025, needs more optimization.
32 372 0.178066563597 Henry Cohn, 2026, needs more optimization.
32 373 0.178265672389 Henry Cohn, 2025, needs more optimization.
32 374 0.178292131328 Henry Cohn, 2025, needs more optimization.
32 375 0.178311620647 Henry Cohn, 2025, needs more optimization.
32 376 0.178315324403 Henry Cohn, 2026, needs more optimization.
32 377 0.178358605451 Henry Cohn, 2025, needs more optimization.
32 378 0.178362988122 Henry Cohn, 2025, needs more optimization.
32 379 0.178383961332 Henry Cohn, 2025, needs more optimization.
32 380 0.179031117557 Henry Cohn, 2026, needs more optimization.
32 381 0.179045766806 Henry Cohn, 2025, needs more optimization.
32 382 0.179092249430 Henry Cohn, 2025, needs more optimization.
32 383 0.179152446284 Henry Cohn, 2025, needs more optimization.
32 384 0.179335801156 Henry Cohn, 2026, needs more optimization.
32 385 0.179356786400 Henry Cohn, 2025, needs more optimization.
32 387 0.179718957095 Henry Cohn, 2025, needs more optimization.
32 388 0.179719254092 Henry Cohn, 2026, needs more optimization.
32 389 0.179852843579 Henry Cohn, 2025, needs more optimization.
32 390 0.179984710270 Henry Cohn, 2025, needs more optimization.
32 392 0.180688469816 Henry Cohn, 2026, needs more optimization.
32 393 0.180975856164 Henry Cohn, 2025, needs more optimization.
32 394 0.181069607451 Henry Cohn, 2025, needs more optimization.
32 395 0.181155096192 Henry Cohn, 2025, needs more optimization.
32 396 0.181231835319 Henry Cohn, 2026, needs more optimization.
32 397 0.181317830477 Henry Cohn, 2025, needs more optimization.
32 398 0.181527503920 Henry Cohn, 2025, needs more optimization.
32 399 0.181848571961 Henry Cohn, 2025, needs more optimization.
32 400 0.181945095808 Henry Cohn, 2026, needs more optimization.
32 401 0.181978777586 Henry Cohn, 2025, needs more optimization.
32 402 0.182219047973 Henry Cohn, 2025, needs more optimization.
32 403 0.182570899265 Henry Cohn, 2025, needs more optimization.
32 404 0.182661426610 Henry Cohn, 2026, needs more optimization.
32 405 0.182835710464 Henry Cohn, 2025, needs more optimization.
32 406 0.182853608628 Henry Cohn, 2025, needs more optimization.
32 407 0.182885908892 Henry Cohn, 2025, needs more optimization.
32 408 0.182925577504 Henry Cohn, 2026, needs more optimization.
32 409 0.183280877984 Henry Cohn, 2025, needs more optimization.
32 410 0.185029828930 Henry Cohn, 2025, needs more optimization.
32 412 0.185037443171 Henry Cohn, 2026, needs more optimization.
32 413 0.185059418161 Henry Cohn, 2025, needs more optimization.
32 414 0.185234156539 Henry Cohn, 2025, needs more optimization.
32 415 0.185270695609 Henry Cohn, 2025, needs more optimization.
32 416 0.185691300174 Henry Cohn, 2026, needs more optimization.
32 417 0.185767568064 Henry Cohn, 2025, needs more optimization.
32 418 0.185793807196 Henry Cohn, 2025, needs more optimization.
32 419 0.185849386954 Henry Cohn, 2025, needs more optimization.
32 420 0.186556419984 Henry Cohn, 2026, needs more optimization.
32 421 0.187264751378 Henry Cohn, 2025, needs more optimization.
32 422 0.187372569965 Henry Cohn, 2025, needs more optimization.
32 423 0.187500608309 Henry Cohn, 2025, needs more optimization.
32 424 0.187677162520 Henry Cohn, 2026, needs more optimization.
32 425 0.187748169214 Henry Cohn, 2025, needs more optimization.
32 426 0.187867093904 Henry Cohn, 2025, needs more optimization.
32 427 0.189248292876 Henry Cohn, 2025, needs more optimization.
32 428 0.189407459282 Henry Cohn, 2026, needs more optimization.
32 429 0.189496872293 Henry Cohn, 2025, needs more optimization.
32 430 0.189519385985 Henry Cohn, 2025, needs more optimization.
32 431 0.189613919573 Henry Cohn, 2025, needs more optimization.
32 432 0.190096051699 Henry Cohn, 2026, needs more optimization.
32 433 0.190140646596 Henry Cohn, 2025, needs more optimization.
32 434 0.190259774616 Henry Cohn, 2025, needs more optimization.
32 435 0.190275021051 Henry Cohn, 2025, needs more optimization.
32 436 0.190279279138 Henry Cohn, 2026, needs more optimization.
32 437 0.190412575829 Henry Cohn, 2025, needs more optimization.
32 438 0.190500167997 Henry Cohn, 2025, needs more optimization.
32 439 0.190594556573 Henry Cohn, 2025, needs more optimization.
32 440 0.190598729392 Henry Cohn, 2026, needs more optimization.
32 442 0.190695092184 Henry Cohn, 2025, needs more optimization.
32 443 0.190970654280 Henry Cohn, 2025, needs more optimization.
32 444 0.191765080937 Henry Cohn, 2026, needs more optimization.
32 445 0.192031953805 Henry Cohn, 2025, needs more optimization.
32 446 0.192165907569 Henry Cohn, 2025, needs more optimization.
32 447 0.192198301060 Henry Cohn, 2025, needs more optimization.
32 448 0.192575448488 Henry Cohn, 2026, needs more optimization.
32 449 0.192604978591 Henry Cohn, 2025, needs more optimization.
32 450 0.193705426727 Henry Cohn, 2025, needs more optimization.
32 451 0.193708611047 Henry Cohn, 2025, needs more optimization.
32 452 0.193764059023 Henry Cohn, 2026, needs more optimization.
32 453 0.193774937757 Henry Cohn, 2025, needs more optimization.
32 454 0.193785864652 Henry Cohn, 2025, needs more optimization.
32 455 0.193793357389 Henry Cohn, 2025, needs more optimization.
32 456 0.193820455278 Henry Cohn, 2026, needs more optimization.
32 457 0.193850961075 Henry Cohn, 2025, needs more optimization.
32 458 0.193882680642 Henry Cohn, 2025, needs more optimization.
32 459 0.193983485564 Henry Cohn, 2025, needs more optimization.
32 460 0.194028782886 Henry Cohn, 2026, needs more optimization.
32 461 0.194081363290 Henry Cohn, 2025, needs more optimization.
32 462 0.194297974813 Henry Cohn, 2025, needs more optimization.
32 463 0.194514027621 Henry Cohn, 2025, needs more optimization.
32 464 0.194671637019 Henry Cohn, 2026, needs more optimization.
32 465 0.194746076501 Henry Cohn, 2025, needs more optimization.
32 467 0.194936725834 Henry Cohn, 2025, needs more optimization.
32 468 0.194981723158 Henry Cohn, 2026, needs more optimization.
32 470 0.195041324171 Henry Cohn, 2025, needs more optimization.
32 471 0.195309985495 Henry Cohn, 2025, needs more optimization.
32 472 0.195329328789 Henry Cohn, 2026, needs more optimization.
32 473 0.195843486350 Henry Cohn, 2025, needs more optimization.
32 476 0.196783837506 Henry Cohn, 2026, needs more optimization.
32 477 0.196868046017 Henry Cohn, 2026, needs more optimization.
32 478 0.196868046050 Henry Cohn, 2025, needs more optimization.
32 480 0.196953029432 Henry Cohn, 2026, needs more optimization.
32 481 0.197048441972 Henry Cohn, 2025, needs more optimization.
32 483 0.197099123339 Henry Cohn, 2025, needs more optimization.
32 484 0.197143227415 Henry Cohn, 2026, needs more optimization.
32 485 0.197177452990 Henry Cohn, 2025, needs more optimization.
32 486 0.197200952183 Henry Cohn, 2025, needs more optimization.
32 488 0.197225446503 Henry Cohn, 2026, needs more optimization.
32 489 0.197286255999 Henry Cohn, 2025, needs more optimization.
32 490 0.197301717432 Henry Cohn, 2025, needs more optimization.
32 491 0.197330090496 Henry Cohn, 2025, needs more optimization.
32 492 0.197343760260 Henry Cohn, 2026, needs more optimization.
32 493 0.197415862215 Henry Cohn, 2025, needs more optimization.
32 494 0.197440959877 Henry Cohn, 2025, needs more optimization.
32 496 0.198146563805 Henry Cohn, 2026, needs more optimization.
32 497 0.198223211211 Henry Cohn, 2026, needs more optimization.
32 498 0.198246760918 Henry Cohn, 2026, needs more optimization.
32 499 0.198539780573 Henry Cohn, 2026, needs more optimization.
32 500 0.198554124984 Henry Cohn, 2026, needs more optimization.
32 501 0.199319841545 Henry Cohn, 2026, needs more optimization.
32 502 0.199319841599 Henry Cohn, 2025, needs more optimization.
32 504 0.199336113389 Henry Cohn, 2026, needs more optimization.
32 508 0.199362959024 Henry Cohn, 2026, needs more optimization.
32 509 0.199378564517 Henry Cohn, 2025, needs more optimization.
32 510 0.199386954560 Henry Cohn, 2025, needs more optimization.
32 512 0.199390912557 Henry Cohn, 2026, needs more optimization.
32 513 0.199399649703 Henry Cohn, 2025, needs more optimization.
32 514 0.199407130962 Henry Cohn, 2025, needs more optimization.
32 515 0.199416557987 Henry Cohn, 2025, needs more optimization.
32 516 0.199426209172 Henry Cohn, 2026, needs more optimization.
32 517 0.199432797025 Henry Cohn, 2025, needs more optimization.
32 518 0.199450104889 Henry Cohn, 2025, needs more optimization.
32 519 0.199507086822 Henry Cohn, 2025, needs more optimization.
32 520 0.199518644335 Henry Cohn, 2026, needs more optimization.
32 524 0.199541335713 Henry Cohn, 2026, needs more optimization.
32 525 0.199554430682 Henry Cohn, 2025, needs more optimization.
32 528 0.199558754784 Henry Cohn, 2026, needs more optimization.
32 529 0.199572873539 Henry Cohn, 2025, needs more optimization.
32 532 0.199587261641 Henry Cohn, 2026, needs more optimization.
32 533 0.199621988169 Henry Cohn, 2025, needs more optimization.
32 534 0.199625963538 Henry Cohn, 2025, needs more optimization.
32 536 0.199681375382 Henry Cohn, 2026, needs more optimization.
32 540 0.199684128978 Henry Cohn, 2026, needs more optimization.
32 543 0.199715301377 Henry Cohn, 2026, needs more optimization.
32 544 0.199732624672 Henry Cohn, 2026, needs more optimization.
32 545 0.199732737568 Henry Cohn, 2026, needs more optimization.
32 548 0.199734949274 Henry Cohn, 2026, needs more optimization.
32 552 0.199745278477 Henry Cohn, 2026, needs more optimization.
32 553 0.199768966540 Henry Cohn, 2025, needs more optimization.
32 554 0.199773953538 Henry Cohn, 2025, needs more optimization.
32 556 0.199774357232 Henry Cohn, 2026, needs more optimization.
32 560 0.199782046435 Henry Cohn, 2026, needs more optimization.
32 564 0.199796886903 Henry Cohn, 2026, needs more optimization.
32 566 0.199821586337 Henry Cohn, 2025, needs more optimization.
32 568 0.199826147563 Henry Cohn, 2026, needs more optimization.
32 572 0.199838559293 Henry Cohn, 2026, needs more optimization.
32 573 0.199857441710 Henry Cohn, 2025, needs more optimization.
32 576 0.199874346564 Henry Cohn, 2026, needs more optimization.
32 577 0.199896658507 Henry Cohn, 2025, needs more optimization.
32 580 0.199897063468 Henry Cohn, 2026, needs more optimization.
32 582 0.199912209372 Henry Cohn, 2025, needs more optimization.
32 584 0.199916090948 Henry Cohn, 2026, needs more optimization.
32 588 0.199924608878 Henry Cohn, 2026, needs more optimization.
32 592 0.199939470789 Henry Cohn, 2026, needs more optimization.
32 593 0.199955171974 Henry Cohn, 2025, needs more optimization.
32 594 0.199965982072 Henry Cohn, 2025, needs more optimization.
32 595 0.199968056167 Henry Cohn, 2025, needs more optimization.
32 596 0.199971184268 Henry Cohn, 2026, needs more optimization.
32 597 0.199999455451 Henry Cohn, 2025, needs more optimization.
32 599 0.199999980426 Henry Cohn, 2025, needs more optimization.
32 600 0.200023969452 Henry Cohn, 2026, needs more optimization.
32 601 0.200078681940 Orthogonal union of 599 points in 31 dimensions and 2 points in 1 dimension.
32 602 0.200177422653 Orthogonal union of 600 points in 31 dimensions and 2 points in 1 dimension.
32 603 0.221586593276 Henry Cohn, 2025, needs more optimization.
32 604 0.221662993664 Henry Cohn, 2026, needs more optimization.
32 605 0.221717120780 Henry Cohn, 2025, needs more optimization.
32 606 0.221813917898 Henry Cohn, 2025, needs more optimization.
32 607 0.222022765006 Henry Cohn, 2025, needs more optimization.
32 608 0.222048835718 Henry Cohn, 2026, needs more optimization.
32 609 0.222537944124 Henry Cohn, 2025, needs more optimization.
32 610 0.222560038881 Henry Cohn, 2025, needs more optimization.
32 611 0.222604300344 Henry Cohn, 2025, needs more optimization.
32 612 0.222837384274 Henry Cohn, 2026, needs more optimization.
32 613 0.222902158393 Henry Cohn, 2025, needs more optimization.
32 614 0.223071161667 Henry Cohn, 2025, needs more optimization.
32 615 0.223421524187 Henry Cohn, 2025, needs more optimization.
32 616 0.223459110719 Henry Cohn, 2026, needs more optimization.
32 617 0.223580573442 Henry Cohn, 2025, needs more optimization.
32 618 0.223636523074 Henry Cohn, 2025, needs more optimization.
32 619 0.224074090101 Henry Cohn, 2025, needs more optimization.
32 620 0.224125087730 Henry Cohn, 2026, needs more optimization.
32 621 0.224198109869 Henry Cohn, 2025, needs more optimization.
32 622 0.224349141028 Henry Cohn, 2025, needs more optimization.
32 623 0.224594176934 Henry Cohn, 2025, needs more optimization.
32 624 0.224628079332 Henry Cohn, 2026, needs more optimization.
32 625 0.224688239800 Henry Cohn, 2025, needs more optimization.
32 626 0.224908630287 Henry Cohn, 2025, needs more optimization.
32 627 0.225052208509 Henry Cohn, 2025, needs more optimization.
32 628 0.225235692634 Henry Cohn, 2026, needs more optimization.
32 629 0.225281047296 Henry Cohn, 2025, needs more optimization.
32 631 0.225529335344 Henry Cohn, 2025, needs more optimization.
32 632 0.225945372898 Henry Cohn, 2026, needs more optimization.
32 633 0.225983394293 Henry Cohn, 2025, needs more optimization.
32 634 0.226044109732 Henry Cohn, 2025, needs more optimization.
32 635 0.226369244528 Henry Cohn, 2025, needs more optimization.
32 636 0.226423782384 Henry Cohn, 2026, needs more optimization.
32 637 0.226562122518 Henry Cohn, 2025, needs more optimization.
32 638 0.226608149926 Henry Cohn, 2025, needs more optimization.
32 639 0.226972193420 Henry Cohn, 2025, needs more optimization.
32 640 0.227007393943 Henry Cohn, 2026, needs more optimization.
32 641 0.227081509842 Henry Cohn, 2025, needs more optimization.
32 642 0.227192756570 Henry Cohn, 2025, needs more optimization.
32 643 0.227375016220 Henry Cohn, 2025, needs more optimization.
32 644 0.227800189903 Henry Cohn, 2026, needs more optimization.
32 645 0.227876477524 Henry Cohn, 2025, needs more optimization.
32 646 0.228180662642 Henry Cohn, 2025, needs more optimization.
32 647 0.228227639935 Henry Cohn, 2025, needs more optimization.
32 648 0.228245509908 Henry Cohn, 2026, needs more optimization.
32 649 0.228297025478 Henry Cohn, 2025, needs more optimization.
32 650 0.228664894603 Henry Cohn, 2025, needs more optimization.
32 651 0.228706321354 Henry Cohn, 2025, needs more optimization.
32 652 0.228750666882 Henry Cohn, 2026, needs more optimization.
32 653 0.229028391919 Henry Cohn, 2025, needs more optimization.
32 654 0.229054054679 Henry Cohn, 2025, needs more optimization.
32 655 0.229370166746 Henry Cohn, 2025, needs more optimization.
32 656 0.229410131495 Henry Cohn, 2026, needs more optimization.
32 657 0.229470677006 Henry Cohn, 2025, needs more optimization.
32 658 0.229577565310 Henry Cohn, 2025, needs more optimization.
32 659 0.229842838967 Henry Cohn, 2025, needs more optimization.
32 660 0.229882266651 Henry Cohn, 2026, needs more optimization.
32 661 0.229937196740 Henry Cohn, 2025, needs more optimization.
32 662 0.230366676017 Henry Cohn, 2025, needs more optimization.
32 663 0.230440116248 Henry Cohn, 2025, needs more optimization.
32 664 0.230444353470 Henry Cohn, 2026, needs more optimization.
32 665 0.230515995016 Henry Cohn, 2025, needs more optimization.
32 666 0.230819239542 Henry Cohn, 2025, needs more optimization.
32 667 0.230873276163 Henry Cohn, 2025, needs more optimization.
32 668 0.230950717621 Henry Cohn, 2026, needs more optimization.
32 669 0.231005292055 Henry Cohn, 2025, needs more optimization.
32 670 0.231105951016 Henry Cohn, 2025, needs more optimization.
32 671 0.231291444753 Henry Cohn, 2025, needs more optimization.
32 672 0.231336958831 Henry Cohn, 2026, needs more optimization.
32 673 0.231602710515 Henry Cohn, 2025, needs more optimization.
32 674 0.231646681715 Henry Cohn, 2025, needs more optimization.
32 675 0.231710945281 Henry Cohn, 2025, needs more optimization.
32 676 0.231766221298 Henry Cohn, 2026, needs more optimization.
32 677 0.231948154617 Henry Cohn, 2025, needs more optimization.
32 678 0.231965445671 Henry Cohn, 2025, needs more optimization.
32 679 0.232051536283 Henry Cohn, 2025, needs more optimization.
32 680 0.232210470967 Henry Cohn, 2026, needs more optimization.
32 681 0.232241559297 Henry Cohn, 2025, needs more optimization.
32 682 0.232259409247 Henry Cohn, 2025, needs more optimization.
32 683 0.232311648171 Henry Cohn, 2025, needs more optimization.
32 684 0.232314107194 Henry Cohn, 2026, needs more optimization.
32 685 0.232346036283 Henry Cohn, 2025, needs more optimization.
32 686 0.232405625384 Henry Cohn, 2026, needs more optimization.
32 687 0.232422487684 Henry Cohn, 2025, needs more optimization.
32 688 0.232514326953 Henry Cohn, 2026, needs more optimization.
32 689 0.232646292853 Henry Cohn, 2025, needs more optimization.
32 690 0.232740739451 Henry Cohn, 2026, needs more optimization.
32 691 0.232784628989 Henry Cohn, 2025, needs more optimization.
32 692 0.232802252433 Henry Cohn, 2026, needs more optimization.
32 693 0.232846649554 Henry Cohn, 2025, needs more optimization.
32 694 0.232851772126 Henry Cohn, 2026, needs more optimization.
32 695 0.232957261911 Henry Cohn, 2025, needs more optimization.
32 696 0.233073726902 Henry Cohn, 2026, needs more optimization.
32 697 0.233088728155 Henry Cohn, 2025, needs more optimization.
32 698 0.233114074855 Henry Cohn, 2026, needs more optimization.
32 699 0.233165875520 Henry Cohn, 2025, needs more optimization.
32 700 0.233211637080 Henry Cohn, 2026, needs more optimization.
32 701 0.233280683689 Henry Cohn, 2025, needs more optimization.
32 702 0.233540630965 Henry Cohn, 2026, needs more optimization.
32 703 0.233574236086 Henry Cohn, 2025, needs more optimization.
32 704 0.233651474269 Henry Cohn, 2026, needs more optimization.
32 705 0.233686743834 Henry Cohn, 2025, needs more optimization.
32 706 0.233791284076 Henry Cohn, 2026, needs more optimization.
32 707 0.234273368337 Henry Cohn, 2025, needs more optimization.
32 708 0.234280236821 Henry Cohn, 2026, needs more optimization.
32 709 0.234358786111 Henry Cohn, 2025, needs more optimization.
32 710 0.234375057971 Henry Cohn, 2026, needs more optimization.
32 711 0.234403334418 Henry Cohn, 2025, needs more optimization.
32 712 0.234408094694 Henry Cohn, 2026, needs more optimization.
32 713 0.234451908934 Henry Cohn, 2025, needs more optimization.
32 714 0.234462957074 Henry Cohn, 2026, needs more optimization.
32 715 0.234508571554 Henry Cohn, 2025, needs more optimization.
32 716 0.234819711583 Henry Cohn, 2026, needs more optimization.
32 717 0.234865960112 Henry Cohn, 2025, needs more optimization.
32 718 0.234988963240 Henry Cohn, 2026, needs more optimization.
32 720 0.235108958563 Henry Cohn, 2026, needs more optimization.
32 722 0.235138065811 Henry Cohn, 2026, needs more optimization.
32 723 0.235160667649 Henry Cohn, 2025, needs more optimization.
32 724 0.235174527831 Henry Cohn, 2026, needs more optimization.
32 725 0.235261358131 Henry Cohn, 2025, needs more optimization.
32 726 0.235301844675 Henry Cohn, 2026, needs more optimization.
32 727 0.235330602148 Henry Cohn, 2025, needs more optimization.
32 728 0.235381651940 Henry Cohn, 2026, needs more optimization.
32 729 0.235411848687 Henry Cohn, 2025, needs more optimization.
32 730 0.235450053802 Henry Cohn, 2026, needs more optimization.
32 732 0.235464780241 Henry Cohn, 2026, needs more optimization.
32 733 0.235501564441 Henry Cohn, 2025, needs more optimization.
32 734 0.235513844868 Henry Cohn, 2026, needs more optimization.
32 735 0.235592448594 Henry Cohn, 2025, needs more optimization.
32 736 0.235653711267 Henry Cohn, 2026, needs more optimization.
32 737 0.236038834283 Henry Cohn, 2025, needs more optimization.
32 738 0.236046607321 Henry Cohn, 2026, needs more optimization.
32 739 0.236099705270 Henry Cohn, 2025, needs more optimization.
32 740 0.236276041096 Henry Cohn, 2026, needs more optimization.
32 742 0.237291473720 Henry Cohn, 2026, needs more optimization.
32 744 0.237344444185 Henry Cohn, 2026, needs more optimization.
32 746 0.237382187309 Henry Cohn, 2026, needs more optimization.
32 747 0.237429998081 Henry Cohn, 2026, needs more optimization.
32 748 0.237434862207 Henry Cohn, 2026, needs more optimization.
32 749 0.237467505111 Henry Cohn, 2026, needs more optimization.
32 750 0.237472600296 Henry Cohn, 2026, needs more optimization.
32 751 0.237503643651 Henry Cohn, 2026, needs more optimization.
32 752 0.237539062019 Henry Cohn, 2026, needs more optimization.
32 754 0.237555021045 Henry Cohn, 2026, needs more optimization.
32 756 0.237596636892 Henry Cohn, 2026, needs more optimization.
32 757 0.237607606558 Henry Cohn, 2026, needs more optimization.
32 758 0.237612646688 Henry Cohn, 2026, needs more optimization.
32 760 0.237622301590 Henry Cohn, 2026, needs more optimization.
32 761 0.237646526637 Henry Cohn, 2025, needs more optimization.
32 762 0.237660115399 Henry Cohn, 2026, needs more optimization.
32 764 0.237910698138 Henry Cohn, 2026, needs more optimization.
32 765 0.237943461008 Henry Cohn, 2026, needs more optimization.
32 766 0.237944630065 Henry Cohn, 2026, needs more optimization.
32 767 0.237963174223 Henry Cohn, 2026, needs more optimization.
32 768 0.237975403324 Henry Cohn, 2026, needs more optimization.
32 769 0.237996834278 Henry Cohn, 2026, needs more optimization.
32 770 0.237998158851 Henry Cohn, 2026, needs more optimization.
32 772 0.238017976129 Henry Cohn, 2026, needs more optimization.
32 774 0.238022777738 Henry Cohn, 2026, needs more optimization.
32 776 0.238030082474 Henry Cohn, 2026, needs more optimization.
32 778 0.238041389628 Henry Cohn, 2026, needs more optimization.
32 780 0.238048209618 Henry Cohn, 2026, needs more optimization.
32 782 0.238058050680 Henry Cohn, 2026, needs more optimization.
32 783 0.238082865036 Henry Cohn, 2025, needs more optimization.
32 1024 0.238095238096 Code with 1024 points in 31 dimensions.
21⁢x−5
52 325* 0.0625 P. J. Cameron, J. M. Goethals, and J. J. Seidel, Strongly regular graphs having strongly regular subconstituents, J. Algebra 55 (1978), 257–280, doi:10.1016/0021-8693(78)90220-X; V. I. Levenshtein, Designs as maximum codes in polynomial metric spaces, Acta Appl. Math. 29 (1992), 1–82, doi:10.1007/BF00053379.
16⁢x−1
64 4224* 0.125 V. I. Levenšteĭn, Bounds for the maximal cardinality of a code with bounded modulus of the inner product (Russian), Dokl. Akad. Nauk SSSR 263 (1982), 1303–1308, English translation in Soviet Math. Dokl. 25 (1982), 526–531; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
8⁢x−1