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This web page contains a table of values of G(n,m) where G(n,m) is the maximum number of ones that can be contained in an n x m Golomb rectangle. Note G(n,m)=G(m,n).

An n by m Golomb rectangle is optimum if it contains G(n,m) ones and this is more than can occur in any smaller Golomb rectangle. When n or m is one optimum Golomb rectangles correspond to Golomb rulers (a 1 by n Golomb rectangle with k ones is the same as a length n-1 Golomb ruler with k marks). Otherwise the table entries achieved by optimum Golomb rectangles link to examples. Additional values of G(n,m) achieved by optimum Golomb rectangles are listed below the table.

For more about Golomb rectangles see my paper Some New Optimum Golomb Rectangles and the references therein.

Table of G(n,m) values
n\m 1 2 3 4 5 6 7 8 9 10 11 12
1 1
2 2 3
3 2 4 5
4 3 4 5 6
5 3 5 6 7 8
6 3 5 6 8 8 9
7 4 5 7 8 9 10 11
8 4 6 8 9 9 11 11 12
9 4 6 8 9 10 11 12 12 13
10 4 7 8 9 10 12 13 13 14 15
11 4 7 9 10 11 12 13 14 14 15 16
12 5 7 9 10 12 13 14 14 15 16 16 17
13 5 7 9 11 12 13 14 15 16 16 17
14 5 8 9 11 12 14 14 15 16 17
15 5 8 10 11 13 14 15 16 16
16 5 8 10 12 13 14 15 16 17
17 5 8 10 12 13 15 16 17
18 6 9 11 12 14 15 16
19 6 9 11 13 14 15 16
20 6 9 11 13 15 16 17

Additional critical values of G(n,m) are listed below linked to examples achieving them.

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