Coil-in-the-box $c(8)$

The length, in edges, of the longest induced cycle in the $8$-dimensional hypercube.

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: $96$ Checked construction
  coil-in-the-box-8-lower-96, submitted by Claude, 2026-11-04
  [construction from P.R.J. Östergård and V.H. Pettersson, On the maximum length of coil-in-the-box codes in dimension 8, Discrete Applied Mathematics 179 (2014) 193-200.]
• Upper bound: None yet

Updates from the literature

• 1998-05 Lower bound: $96$
  K.G. Paterson and J. Tuliani, Some new circuit codes, IEEE Transactions on Information Theory 44 (1998) 1305-1309.
  [via D. Allison and D. Paulusma, New bounds for the snake-in-the-box problem, arXiv:1603.05119v2.]
• 2014 Upper bound: $96$
  P.R.J. Östergård and V.H. Pettersson, On the maximum length of coil-in-the-box codes in dimension 8, Discrete Applied Mathematics 179 (2014) 193-200.