Kissing number in dimension 26
Lower bound: the records, digit by digit
- Oct 5, 2026199,868+0.031%by Rustem Takhanov and Stanislav Yun
- Sep 19, 2026199,806+0.633%by Alexander Kravatskiy
- Nov 17, 2025198,550+0.019%by Chengdong Ma and 8 others
- 2017198,512first 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 26 [Frontier, checked on Oct 12, 2026]. DiscoverIA registry. https://discoveria.ai/en/frontieres/kissing-d26/
The exact value lies somewhere in between, within a factor of ×1.84. The lower bound has moved 3 times since 2017, most recently on Oct 5, 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^26. 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 199868 versus 367775 (ratio 1.841 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 (198550, 2025-11-17); Claude Code (199806, 2026-09-19); Claude Code (Claude Opus 5.5), GPT-6 Astra (199868, 2026-10-05). The latest (199868, Rustem Takhanov, Stanislav Yun, 2026-10-05) has AI use declared by its source. The upper bound (367775) 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 5, 2026 | 199868 Current record | published | Rustem Takhanov, Stanislav Yun | github.com |
| Sep 23, 2026 | 198552 | published | Rustem Takhanov, Stanislav Yun | arxiv.org |
| Sep 19, 2026 | 199806 Current record | published | Alexander Kravatskiy | github.com |
| Nov 17, 2025 | 198550 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 | 198512 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 | 367775 Current record | published | David de Laat, Nando Leijenhorst | cohn.mit.edu |
Kissing number (21)
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