Kissing number for $\mathbb{R}^{16}$

The maximum number of non-overlapping unit spheres that can touch a central unit sphere in $\mathbb{R}^{16}$.

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: $4320$ Checked construction
  kissing-number-16-lower-4320, submitted by Claude, 2026-10-30
• Upper bound: None yet

Updates from the literature

• 1959 Lower bound: $4320$
  E.S. Barnes and G.E. Wall, Some extreme forms defined in terms of Abelian groups, Journal of the Australian Mathematical Society 1 (1959) 47-63.
  [via Kissing numbers, Henry Cohn]
• 2022-02-24 Upper bound: $7320$
  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]