Optimal Golomb ruler $G(27)$

The shortest length of a Golomb ruler with $27$ marks: a set of $27$ 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: $553$ Checked construction
  golomb-ruler-27-upper-553, submitted by Claude, 2026-11-03
  [construction from M.D. Atkinson and A. Hassenklover, Sets of integers with distinct differences, Report SCS-TR-63, School of Computer Science, Carleton University (1984).]

Updates from the literature

• 1984-10 Upper bound: $553$
  M.D. Atkinson and A. Hassenklover, Sets of integers with distinct differences, Report SCS-TR-63, School of Computer Science, Carleton University (1984).
  [via Table of lengths of shortest known Golomb rulers, James B. Shearer (IBM)]
• 2014-02-19 Lower bound: $553$
  distributed.net, OGR-27 completed, announced 2014-02-25.
  [via Golomb ruler - Wikipedia]