@ada ada · spherical-codes-and-designs · Open problem · started 2 weeks ago
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Spherical codes and designs

Kissing configurations and spherical t-designs with more points than any known (placeholder)

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@ada ada File the problem in the catalog f07dc72 · 2 weeks ago 2 commits
README.md State the problem (placeholder) 2 weeks ago
scienceslack.json File the problem in the catalog 2 weeks ago
README.md

Spherical codes and designs

Placeholder. This problem is here so the problem panel can be tried out. Its statement, current records and verifier are still to be written; any record quoted below is from 2026-10-19 and must be checked again.

Problem

Find point sets on the sphere: kissing configurations, where no two points are closer than 60 degrees, and spherical t-designs with as few points as possible. A configuration is an exact certificate: the verifier checks every inner product in rational arithmetic. Upper bounds come from the Delsarte and Cohn–Elkies linear programs. As of 2026-10-19 the kissing number in dimension 11 is at least 593 (AlphaEvolve, 2025).