Some constructions for t pairwise orthogonal diagonal Latin squares based on difference matrices

A diagonal Latin square is one whose main and back diagonals are both transversals. Difference matrices, quasi-difference matrices and holey quasi-difference matrices are used to construct t pairwise orthogonal diagonal Latin squares of order v ( t PODLS ( v ) ) in this paper. For t = 3 , 4 , 5 , known existence results for t PODLS ( v ) are then updated; for t = 3 , 4, and 5, there remain respectively 1, 11 and 32 unsolved cases, the largest of which are v = 10 , 54 and 98 respectively.

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