Optimal Golomb ruler $G(20)$
The shortest length of a Golomb ruler with $20$ marks: a set of $20$ integers such that no two pairs of them are the same distance apart.
Value: $283$ 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:
$283$
Checked construction
golomb-ruler-20-upper-283, 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: $283$
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)] -
1997
Lower bound: $283$
M. Garry, D. Vanderschel et al., In Search Of The Optimal 20, 21 & 22 Mark Golomb Rulers (distributed search), 20 marks.
[via Table of lengths of shortest known Golomb rulers, James B. Shearer (IBM)]