The number of different reduced complete sets of MOLS corresponding to PG (2,q)

In the first part of this article we determine the exact number of different reduced complete sets of mutually orthogonal latin squares (MOLS) of order q, for q = p(d), p prime, d >= 1, corresponding to the Desarguesian projective planes PG(2, q). In the second part we provide some computational results and enumerate the maximal sets of reduced latin squares of order n as part of a set containing exactly r MOLS