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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