Classification of difference matrices over cyclic groups

The existence of difference matrices over small cyclic groups is investigated in this computer-aided work. The maximum values of the parameters for which difference matrices exist as well as the number of inequivalent difference matrices in each case is determined up to the computational limit. Several new difference matrices have been found in this manner. The maximum number of rows is 9 for an r   ×15 difference matrix over Z3Z3, 8 for an r   ×15 difference matrix over Z5Z5, and 6 for an r   ×12 difference matrix over Z6Z6; the number of inequivalent matrices with these parameters is 5, 2, and 7, respectively.