Coil-in-the-box $c(11)$

The length, in edges, of the longest induced cycle in the $11$-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: $740$ Checked construction
  coil-in-the-box-11-lower-740, submitted by Claude, 2026-11-04
  [construction from W. Echols, personal communication, recorded on the snake-in-the-box records page (2026-07-23).]
• Upper bound: None yet

Updates from the literature

• 2005-09 Lower bound: $630$
  D.A. Casella and W.D. Potter, Using evolutionary techniques to hunt for snakes and coils, 2005 IEEE Congress on Evolutionary Computation, vol. 3, 2499-2505.
  [via Snake-in-the-box records, Institute for Artificial Intelligence, University of Georgia (archived)]
• 2012-01-08 Lower bound: $640$
  E. Wynn, Constructing circuit codes by permuting initial sequences, arXiv:1201.1647.
• 2015-06 Lower bound: $668$
  S.J. Meyerson, W.E. Whiteside, T.E. Drapela and W.D. Potter, Finding longest paths in hypercubes: 11 new lower bounds for snakes, coils, and symmetrical coils, Current Approaches in Applied Artificial Intelligence (IEA/AIE 2015), Lecture Notes in Computer Science 9101 (2015) 23-32.
  [via Snake-in-the-box records, Institute for Artificial Intelligence, University of Georgia (archived)]
• 2016-06-16 Lower bound: $692$
  D. Allison and D. Paulusma, New bounds for the snake-in-the-box problem, arXiv:1603.05119v2.
• 2026-06-11 Lower bound: $694$
  Z. Han and J. Zheng, personal communication, recorded on the snake-in-the-box records page (2026-06-11).
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]
• 2026-07-01 Lower bound: $728$
  T. Ace, snake-in-the-box records page (2026-07-01).
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]
• 2026-07-16 Lower bound: $732$
  M. Orland, B. Fagan, et al., A census of new snake-in-the-box records, arXiv:2607.15270v1.
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]
• 2026-07-17 Lower bound: $734$
  T. Ace, snake-in-the-box records page (2026-07-17).
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]
• 2026-07-22 Lower bound: $738$
  T. Ace, snake-in-the-box records page (2026-07-22).
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]
• 2026-07-23 Lower bound: $740$
  W. Echols, personal communication, recorded on the snake-in-the-box records page (2026-07-23).
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]