Kissing number in dimension 28
Lower bound: the records, digit by digit
- Oct 10, 2026205,172+0.135%by Kevin Li
- Sep 15, 2026204,896+0.184%by Alexander Kravatskiy
- Nov 17, 2025204,520+0.074%by Chengdong Ma and 8 others
- 2017204,368first recordby Kenz Kallal and 2 others
Coloured and underlined: the digits that changed since the previous record. No chart: since the first published record, neither bound has moved by more than 5% of the gap between them.
Cite this frontier
DiscoverIA. Kissing number in dimension 28 [Frontier, checked on Oct 12, 2026]. DiscoverIA registry. https://discoveria.ai/en/frontieres/kissing-d28/
The exact value lies somewhere in between, within a factor of ×3.67. The lower bound has moved 3 times since 2017, most recently on Oct 10, 2026. The upper bound has not moved since 2024.
The maximum number of unit spheres with disjoint interiors that can touch a central unit sphere in R^28. A valid configuration of N spheres gives the lower bound N; a linear or semidefinite programming bound gives an upper bound.
Exact value unknown: gap 205172 versus 752292 (ratio 3.667 on Cohn's table consulted 2026-10-13). Lower bounds are explicit constructions (the recent ones announce an exact-arithmetic program check); no named third-party review appears in the sources read. The sources read declare AI use for these lower bounds: PackingStar (204520, 2025-11-17); Claude Code (204896, 2026-09-15); GPT-6-Astra Pro, Claude Opus 5.5 (205172, 2026-10-10). The latest (205172, Kevin Li, 2026-10-10) has AI use declared by its source. The upper bound (752292) is a semidefinite programming bound (Cohn's table, credited to Leijenhorst-de Laat); no source read attributes it to an AI.
Every step, as a table : Lower bound (5 points)
Best known configuration (constructions), from the Leech, Kallal-Kan-Wang or Cohn-Li records to the AI-assisted constructions of 2025-2026.
| Date | Exact value | Nature | Authors | Source |
|---|---|---|---|---|
| Oct 10, 2026 | 205172 Current record | published | Kevin Li | github.com |
| Sep 23, 2026 | 204522 | published | Rustem Takhanov, Stanislav Yun | arxiv.org |
| Sep 15, 2026 | 204896 Current record | published | Alexander Kravatskiy | github.com |
| Nov 17, 2025 | 204520 Current record | published | Chengdong Ma, Théo Tao Zhaowei, Pengyu Li, Minghao Liu, Haojun Chen, Zihao Mao, Yuan Cheng, Yuan Qi, Yaodong Yang | arxiv.org |
| 2017 | 204368 Current record | published | Kenz Kallal, Tomoka Kan, Eric Wang | doi.org |
Every step, as a table : Upper bound (1 points)
Best known upper bound (three-point semidefinite programming).
| Date | Exact value | Nature | Authors | Source |
|---|---|---|---|---|
| 2024 | 752292 Current record | published | David de Laat, Nando Leijenhorst | cohn.mit.edu |
Kissing number (21)
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