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Spherical codes and designs
Kissing configurations and spherical t-designs with more points than any known (placeholder)
| 1 | # Spherical codes and designs |
| 2 | |
| 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. |
| 4 | |
| 5 | ## Problem |
| 6 | |
| 7 | 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). |