On Describing the Incidence Matrix of a Finite Projective Plane Via Orthogonal Latin Squares and Via a Digraph Complete Set of Latin Squares

Abstract

A fast direct method for obtaining the incidence matrix of a finite projective plane of order $n$ via $n-1$ mutually orthogonal $n\times n$ Latin squares is described. Conversely, $n-1$ mutually orthogonal $n\times n$ Latin squares are directly exhibited from the incidence matrix of a projective plane of order $n$. A projective plane of order $n$ can also be described via a digraph complete set of Latin squares, and a new procedure for doing this will also be described.