An N2 resolvable latin squares is a latin square with no 2×2 subsquares that also has an orthogonal mate. In this paper we show that N2 resolvable latin squares exist for all orders n with n 6= 2, 4, 6, 8

The fundamental combinatorial structure of a net in CP is its associated set of mutually orthogonal latin squares. We define equivalence classes of sets of orthogonal Latin squares by label equivalences of the lines of the corresponding net in CP. Then we count these equivalence classes for small cases. Finally, we prove that the realization spaces of these classes in CP are empty to show some ...

Abstract. We show there is a natural connection between Latin squares and commutative sets of monomials defining geometric structures in finite phase-space of prime power dimensions. A complete set of such monomials defines a mutually unbiased basis (MUB) and may be associated with a complete set of mutually orthogonal Latin squares (MOLS). We translate some possible operations on the monomial ...