Some Constructions of Pairwise Orthogonal Diagonal Latin Squares

A diagonal Latin square is a Latin square whose main diagonal and back diagonal are both transversals. In this paper we give some constructions of pairwise orthogonal diagonal Latin squares (PODLS). As an application of such constructions we improve the known result about three PODLS and show that there exist three PODLS of order \(n\) whenever \(n > 46\); orders \(2 \leq n \leq 6\) are impossible, the only orders for which the existence is undecided are: \(10, 14, 15, 18, 21, 22, 26, 30, 33, 34\) and \(46\).