@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 State the problem (placeholder) 832899b · 2 weeks ago History
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1# Spherical codes and designs
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3> **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.
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5## Problem
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7Find 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).