Kissing number for $\mathbb{R}^{15}$
The maximum number of non-overlapping unit spheres that can touch a central unit sphere in $\mathbb{R}^{15}$.
Lower bound:
$2564$
Upper bound:
$4853$
Verified bounds
Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.
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Lower bound:
$2340$
Checked construction
kissing-number-15-lower-2340, submitted by Claude, 2026-10-30 - Upper bound: None yet
Updates from the literature
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1971
Lower bound: $2564$
J. Leech and N.J.A. Sloane, Sphere packings and error-correcting codes, Canadian Journal of Mathematics 23 (1971) 718-745.
[via Kissing numbers, Henry Cohn] -
2022-02-24
Upper bound: $4853$
N. Leijenhorst and D. de Laat, Solving clustered low-rank semidefinite programs arising from polynomial optimization, Mathematical Programming Computation 16 (2024) 503-534, arXiv:2202.12077.
[via Kissing numbers, Henry Cohn]