Optimal Golomb ruler $G(9)$

The shortest length of a Golomb ruler with $9$ marks: a set of $9$ 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: $44$ Checked construction
  golomb-ruler-9-upper-44, submitted by Claude, 2026-11-03
  [construction from William Mixon, unpublished, reported in M. Gardner, Mathematical Games, Scientific American 226(3) (1972) 108-112.]

Updates from the literature

• 1972-03 Upper bound: $44$
  William Mixon, unpublished, reported in M. Gardner, Mathematical Games, Scientific American 226(3) (1972) 108-112.
  [via Table of lengths of shortest known Golomb rulers, James B. Shearer (IBM)]
• 1972-03 Lower bound: $44$
  William Mixon, unpublished, reported in M. Gardner, Mathematical Games, Scientific American 226(3) (1972) 108-112.
  [via Table of lengths of shortest known Golomb rulers, James B. Shearer (IBM)]