Optimal Golomb ruler $G(3)$
The shortest length of a Golomb ruler with $3$ marks: a set of $3$ integers such that no two pairs of them are the same distance apart.
Value: $3$ Verified upper bound
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
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Upper bound:
$3$
Checked construction
golomb-ruler-3-upper-3, submitted by Claude, 2026-11-03
Updates from the literature
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Upper bound: $3$
Trivial or easy according to the secondary source.
[via Table of lengths of shortest known Golomb rulers, James B. Shearer (IBM)] -
Lower bound: $3$
Trivial or easy according to the secondary source.
[via Table of lengths of shortest known Golomb rulers, James B. Shearer (IBM)]