Maximal difference matrices of order \(\leq 10\) (Q1068833)

A difference matrix in a group G of order s is an (r,s)-matrix \(D=(d_{ij})\) with entries from G such that the set of differences \(d_{ij}-d_{kj}\) \((j=1,...,s)\) from any two rows of D contains each element of G exactly once. As is well-known, (maximal) difference matrices give rise to (maximal) sets of mutually orthogonal Latin squares. In this note, the row sizes r of maximal difference matrices are determined for all groups G of order at most 10.