Kissing number in dimension 30
Lower bound: the records, digit by digit
- Oct 10, 2026222,072+0.48%by Kevin Li
- Sep 17, 2026221,012+0.259%by Alexander Kravatskiy
- Nov 17, 2025220,440+0.207%by Chengdong Ma and 8 others
- 2017219,984first 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 30 [Frontier, checked on Oct 12, 2026]. DiscoverIA registry. https://discoveria.ai/en/frontieres/kissing-d30/
The exact value lies somewhere in between, within a factor of ×6.92. 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^30. 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 222072 versus 1537707 (ratio 6.925 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 (220440, 2025-11-17); Claude Code (221012, 2026-09-17); GPT-6-Astra Pro, Claude Opus 5.5 (222072, 2026-10-10). The latest (222072, Kevin Li, 2026-10-10) has AI use declared by its source. The upper bound (1537707) 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 | 222072 Current record | published | Kevin Li | github.com |
| Sep 23, 2026 | 220442 | published | Rustem Takhanov, Stanislav Yun | arxiv.org |
| Sep 17, 2026 | 221012 Current record | published | Alexander Kravatskiy | github.com |
| Nov 17, 2025 | 220440 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 | 219984 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 | 1537707 Current record | published | David de Laat, Nando Leijenhorst | cohn.mit.edu |
Kissing number (21)
Report an error or suggest a source
Thank you, your message was sent.
Sending failed. Try again, or write to [email protected].