The number of different reduced complete sets of MOLS corresponding to PG $$\varvec{(2,q)}$$ ( 2 , q )

Abstract

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, $$d \ge 1$$ , 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.