Optimal Golomb ruler $G(19)$
The shortest length of a Golomb ruler with $19$ marks: a set of $19$ integers such that no two pairs of them are the same distance apart.
Value: $246$ 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:
$246$
Checked construction
golomb-ruler-19-upper-246, 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
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1967-01
Upper bound: $246$
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)] -
1998-01
Lower bound: $246$
A. Dollas, W.T. Rankin and D. McCracken, A new algorithm for Golomb ruler derivation and proof of the 19 mark ruler, IEEE Transactions on Information Theory 44 (1998) 379-382.
[via Table of lengths of shortest known Golomb rulers, James B. Shearer (IBM)]