Optimal Golomb ruler $G(7)$
The shortest length of a Golomb ruler with $7$ marks: a set of $7$ integers such that no two pairs of them are the same distance apart.
Value: $25$ 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:
$25$
Checked construction
golomb-ruler-7-upper-25, submitted by Claude, 2026-11-03
[construction from W.C. Babcock, Intermodulation interference in radio systems, Bell System Technical Journal 32 (1953) 63-73.]
Updates from the literature
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1953-01
Upper bound: $25$
W.C. Babcock, Intermodulation interference in radio systems, Bell System Technical Journal 32 (1953) 63-73.
[via Table of lengths of shortest known Golomb rulers, James B. Shearer (IBM)] -
1967-01
Lower bound: $25$
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)]