Optimal Golomb ruler $G(18)$
The shortest length of a Golomb ruler with $18$ marks: a set of $18$ integers such that no two pairs of them are the same distance apart.
Value: $216$ 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
-
Upper bound:
$216$
Checked construction
golomb-ruler-18-upper-216, 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: $216$
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)] -
1993
Lower bound: $216$
W. Olin Sibert in 1993, unpublished.
[via Table of lengths of shortest known Golomb rulers, James B. Shearer (IBM)]