Kissing number in dimension 18

8358≤ value ≤16,406lower boundupper bound

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Feb 24, 2022upper bound 16,406by David de Laat and Nando Leijenhorstarxiv.org
Nov 7, 2024lower bound 7654by Henry Cohn and Anqi Liarxiv.org
Sep 16, 2026lower bound 8358by Alexander Kravatskiygithub.com
Oct 12, 2026Last checked

Lower bound · published · Sep 16, 2026

Exact value : 8358

Kravatskiy : 8358 en dimension 18 (hexagone de cosets « bent » sur le réseau de Barnes-Wall impair) · github.com

by Alexander Kravatskiy

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DiscoverIA. Kissing number in dimension 18 [Frontier, checked on Oct 12, 2026]. DiscoverIA registry. https://discoveria.ai/en/frontieres/kissing-d18/

The exact value lies somewhere in between, within a factor of ×1.96. The lower bound has moved 2 times since 1967, most recently on Sep 16, 2026. The upper bound has not moved since 2022.

The maximum number of unit spheres with disjoint interiors that can touch a central unit sphere in R^18. 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 8358 versus 16406 (ratio 1.963 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: Claude Code (8358, 2026-09-16). The latest (8358, Alexander Kravatskiy, 2026-09-16) has AI use declared by its source. The upper bound (16406) 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 (3 points)

Best known configuration (constructions), from the Leech, Kallal-Kan-Wang or Cohn-Li records to the AI-assisted constructions of 2025-2026.

Points : Lower bound
Date	Exact value	Nature	Authors	Source
Sep 16, 2026	`8358` Current record	published	Alexander Kravatskiy	github.com
Nov 7, 2024	`7654` Current record	published	Henry Cohn, Anqi Li	arxiv.org
1967	`7398` Current record	published	John Leech	doi.org

Every step, as a table : Upper bound (1 points)

Best known upper bound (three-point semidefinite programming).

Points : Upper bound
Date	Exact value	Nature	Authors	Source
Feb 24, 2022	`16406` Current record	published	David de Laat, Nando Leijenhorst	arxiv.org

Kissing number (21)

Kissing number in dimension 18

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