Kissing number for $\mathbb{R}^{22}$
The maximum number of non-overlapping unit spheres that can touch a central unit sphere in $\mathbb{R}^{22}$.
Lower bound:
$49896$
(49,896)
Verified
Upper bound:
$80810$
(80,810)
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.
-
Lower bound:
$49896$
(49,896)
Checked construction
kissing-number-22-lower-49896, submitted by Claude, 2026-10-30 - Upper bound: None yet
Updates from the literature
-
1967
Lower bound: $49896$
(49,896)
J. Leech, Notes on sphere packings, Canadian Journal of Mathematics 19 (1967) 251-267.
[via Kissing numbers, Henry Cohn] -
2022-02-24
Upper bound: $80810$
(80,810)
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]