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If $g=1$, these are also called $B_2$-sets, Sidon sets, and Babcock sets. We define $G(g,n)$ to represent the minimum diameter of a $g$-Golomb Ruler. In this paper, we prove that for all $b\\ge 1$, if $g \\ge \\frac{7}{4}\\left(b^{3/2} -b\\right)+1,$ then $G(g,g+b)=g+2b-2$. Sharper bounds are given for $b\\le 18$. The main technique is through an arithmetic property of the integers that are \\emph{not} in a $g$-Golomb ruler, leading us to intr","authors_text":"Aditya Gupta, Kevin O'Bryant","cross_cats":[],"headline":"For g at least roughly 1.75 times b to the 3/2 power, the shortest g-Golomb ruler with g plus b marks has diameter exactly g plus 2b minus 2.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-14T00:47:08Z","title":"Optimal Diameters of High Multiplicity g-Golomb Rulers"},"references":{"count":8,"internal_anchors":0,"resolved_work":8,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"M. D. Atkinson and A. Hassenklover,Sets of integers with distinct differences, Sch Comput. Sci. (Aug 1984). Rep. SCS-TR-63. 14","work_id":"62975abe-5a71-4627-86e3-f40c0a6ae5be","year":1984},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"M. D. Atkinson, N. Santoro, and J. 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