Exact determination of Golomb ruler lengths

Determine the exact minimum length of a Golomb ruler with n marks for every natural number n, thereby solving the Golomb ruler problem beyond the currently known values and available upper and lower bounds.

Background

The Golomb ruler problem asks for the smallest possible length of a set of n integers whose pairwise differences are all distinct. The paper explains that exact values are known only for small values of n, while researchers have established upper and lower bounds for general n. Determining the exact function for all n remains unresolved and is representative of the extremal-combinatorial problems included in SqueezeBench.

References

Although there is no known solution for the Golomb ruler problem for all possible values of n, researchers have proved upper and lower bounds on these numbers [Singer, 1938, Erdős and Turán, 1941, Lindström, 1969].

— SqueezeBench: Saturation-Resilient Evaluation of Mathematical Capability  (2610.13461 - Manrique et al., 9 Oct 2026) in Section 2, Framework, subsection “Problems.”