Ten spherical codes in dimensions 11 to 17 that improved Henry Cohn's table of spherical codes

Ten spherical codes in dimensions 11 to 17, submitted to Henry Cohn's table of spherical codes (spherical-codes.org, archived at hdl.handle.net/1721.1/153543) on 19 October 2026. Each one improved the table entry for its (d, N) on that date. On 29 October 2026 six are still the table entries, credited "Antoine Olivier, 2026". The other four have since been improved by Henry Cohn (entries marked "needs more optimization") and are kept here as submitted. Nothing is claimed about optimality. Results Each file holds N nonzero vectors of R^d, which give N points on the unit sphere after normalisation. The value c bounds the maximal pairwise cosine of the normalised points: max cos <= c, so the minimal angle is at least arccos(c). Lower is better. Six codes that are still the table entry on 29 October: (d, N)Table on 19 OctThis work (c) (11, 82)0.2630188786760.263018342364 (12, 66)0.2147270522100.214718112242 (12, 92)0.2583745976770.258276397340 (13, 72)0.2054225842820.205422579377 (14, 76)0.1898829812780.189882980940 (14, 80)0.1955665651020.195566522972 Four codes since improved by Henry Cohn: (d, N)Table on 19 Oct, then this work (c)Table on 29 Oct (13, 95)0.244179109624, then 0.2440978603770.244097856927 (15, 75)0.168258837686, then 0.1682557198710.168255719819 (17, 83)0.149982620206, then 0.1499705768010.149970574468 (17, 84)0.149995256047, then 0.1499931598210.149993147703 The 19 October column is the table read before the upload. On that date (12,92) was credited to Ilmari Vahteristo, (13,95) to Luke Granto, (17,83) to Robert Dallara, and the other seven entries to Henry Cohn. Method Local polishing by sequential linear programming. Eight entries start from Henry Cohn's entry marked "needs more optimization"; (17,83) starts from Henry Cohn's code as shown on 17 October 2026. (12,92) and (13,95) start from the table entry for (d, N+1) with one point removed: (12,93) by Ilmari Vahteristo (arXiv:2610.19988), and (13,96), credited to Luke Granto on 19 October. The four codes later improved by Henry Cohn were still improving slightly in the author's last polishing pass. Verification Each value c is the exact maximal cosine rounded up at the twelfth decimal: c - 1e-12 < max cos <= c. Each coordinate is an integer divided by 2^52, written exactly as a decimal, so the check involves no rounding. Two separately written programs, each holding the ten values of c, read every coordinate as an exact rational and test every pair. check_spherical.py was written with Claude Opus 5.5 under the author's direction. verify_deepseek.py was written by DeepSeek V4.1 Flash from the statement and the file format alone, without seeing check_spherical.py. It is included unchanged. On 29 October 2026 both accepted the ten files and found the same maximal pairs. Both rejected, with exit code 1, the six corrupted copies of 11_82.txt written by make_controls.py: a repeated vector; one vector of the worst pair moved so that the pair's cosine is c + 9.3e-7; a missing line; CRLF line endings; a zero vector; a coordinate in scientific notation. On 19 October, before the upload, two other exact programs (Python and PARI/GP) had checked the integer files (coordinates times 2^52). Those files and programs are not included. Files Ten files <d>_<N>.txt, one vector per line, d comma-separated decimals. The vectors are not normalised; the cosine does not depend on scale. check_spherical.py, verify_deepseek.py, make_controls.py. README.txt and SHA256SUMS. Limits The comparison is with Henry Cohn's table on the dates above. A better code may exist elsewhere. Use of AI The codes, the computations and check_spherical.py were produced with Claude Opus 5.5 (Anthropic) in Claude Code under the author's direction. verify_deepseek.py was written by DeepSeek V4.1 Flash. The author is responsible for the deposit. No AI system is an author.