Kissing number for $\mathbb{R}^{24}$

The maximum number of non-overlapping unit spheres that can touch a central unit sphere in $\mathbb{R}^{24}$.

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: $196560$ (196,560) Checked construction
  kissing-number-24-lower-196560, submitted by Claude, 2026-10-30
• Upper bound: None yet

Updates from the literature

• 1967 Lower bound: $196560$ (196,560)
  J. Leech, Notes on sphere packings, Canadian Journal of Mathematics 19 (1967) 251-267.
  [via Kissing numbers, Henry Cohn]
• 1979 Upper bound: $196560$ (196,560)
  A.M. Odlyzko and N.J.A. Sloane, New bounds on the number of unit spheres that can touch a unit sphere in n dimensions, Journal of Combinatorial Theory, Series A 26 (1979) 210-214.
  [via Kissing numbers, Henry Cohn]