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This web page is devoted to disjoint Golomb rulers.

Klove ( TK ) defined H(I,J) to be the smallest n such that there are I disjoint Golomb rulers each containing J marks chosen from {1,2,...,n}. The table lists some of the exactly known values of H(I,J). Values equal to the trivial lower bound I*J (which holds for I sufficiently large) are marked with a *.

Table 1 - Exact values of H(I,J)
J\I 1 2 3 4 5 6 7 8 9
1 1* T 2* TK 3* TK 4* TK 5* TK 6* TK 7* TK 8* TK 9* TK
2 2* T 4* TK 6* TK 8* TK 10* TK 12* TK 14* TK 16* TK 18* TK
3 4 T 6* TK 9* TK 12* TK 15* TK 18* TK 21* TK 24* TK 27* TK
4 7 T 9 TK 12* TK 16* TK 20* TK 24* TK 28* TK 32* TK 36* TK
5 12 T 13 TK 16 TK 20* TK 25* TK 30* TK 35* TK 40* TK 45* TK
6 18 T 19 TK 21 TK 24* TK 30* TK 36* TK 42* TK 48* TK 54* TK
7 26 T 27 TK 30 JS 32 JS 35* JS 42* TK 49* TK 56* TK 63* TK
8 35 T 37 JS 38 JS 41 JS 44 JS 48* JS 56* JS 64* TK 72* TK
9 45 T 46 JS 49 JS 52 JS 54 JS 58 JS 63* JS 72* JS 81* JS
10 56 T 59 JS 61 JS 64 JS 67 JS 70 JS
11 73 T 75 JS 77 JS 80 JS 82 JS 85 JS
12 86 T 89 JS 92 JS 96 JS 98 JS 101 JS
13 107 T 108 JS 113 JS 115 JS 118 JS 121 JS

References for the table above.

T - trivial
Values H(1,J) are equal to the the length of the minimum Golomb ruler with J marks plus 1 (since the smallest position is 1 not 0).
TK - Torleiv Klove
T. Klove, "Bounds and Constructions of Disjoint Sets of Distinct Difference Sets", IEEE Transactions on Information Theory, 36(1990), p. 184-190
JS - James B. Shearer
J. B. Shearer, "Some New Disjoint Golomb Rulers", IEEE Transactions on Information Theory, 44(1998), p. 3151-3153.

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