Optimal Golomb ruler $G(10)$
The shortest length of a Golomb ruler with $10$ marks: a set of $10$ integers such that no two pairs of them are the same distance apart.
Value: $55$ 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:
$55$
Checked construction
golomb-ruler-10-upper-55, 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: $55$
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)] -
1972-03
Lower bound: $55$
William Mixon, unpublished, reported in M. Gardner, Mathematical Games, Scientific American 226(3) (1972) 108-112.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)]