The kissing number in dimension 19
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The kissing number k(19) is the largest number of nonoverlapping unit spheres that can touch one unit sphere in nineteen-dimensional Euclidean space. The construction target is a larger certified configuration; the reported lower bound is 11,948.
Why it matters and what counts as progress
Why it matters: It narrows a fixed-dimensional sphere-packing gap through exact feasible configurations rather than a claim of optimality.
What counts as progress: A larger rigorously feasible kissing configuration in dimension 19, a lower upper bound, or matching bounds determining the exact value.
How the problem developed
- 7 Nov 2024 · Lower bound [1]
Henry Cohn and Anqi Li Improved the dimension-19 lower bound to 10,668 using a modified Leech-lattice construction; this remained a lower bound, not an exact value.
- 11 Mar 2026 · Lower bound [2]
Boon Suan Ho Raised the dimension-19 lower bound to 11,948 with a code construction inside a punctured extended Golay code.
AI contribution
A new lower bound for the kissing number in 19 dimensions
A 1,280-word binary code of length 19 and minimum distance five inside a five-punctured extended Golay code extends Cohn and Li’s 10,668-point configuration. It gives the lower bound k(19)≥11,948.
Sources
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