Optimal Golomb ruler $G(30)$

Shortest known Golomb ruler with 30 marks

The shortest length of a Golomb ruler with $30$ marks: a set of $30$ integers such that no two pairs of them are the same distance apart.

Lower bound: Unknown
Upper bound: $680$ Verified

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: $680$ Checked construction
golomb-ruler-30-upper-680, 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: $680$
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)]