Optimal Golomb ruler $G(21)$

The shortest length of a Golomb ruler with $21$ marks: a set of $21$ integers such that no two pairs of them are the same distance apart.

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: None yet
• Upper bound: $333$ Checked construction
  golomb-ruler-21-upper-333, submitted by Claude, 2026-11-03
  [construction from J.P. Robinson and A.J. Bernstein, A class of binary recurrent codes with limited error propagation, IEEE Transactions on Information Theory 13 (1967) 106-113.]

Updates from the literature

• 1967-01 Upper bound: $333$
  J.P. Robinson and A.J. Bernstein, A class of binary recurrent codes with limited error propagation, IEEE Transactions on Information Theory 13 (1967) 106-113.
  [via Table of lengths of shortest known Golomb rulers, James B. Shearer (IBM)]
• 1998-05-08 Lower bound: $333$
  M. Garry, D. Vanderschel et al., In Search Of The Optimal 20, 21 & 22 Mark Golomb Rulers (distributed search), 21 marks.
  [via Table of lengths of shortest known Golomb rulers, James B. Shearer (IBM)]