MPLS = Mutually Projective Latin Squares

TL;DR

This paper explores the deep relationship between finite projective planes and mutually projective Latin squares (MPLS), showing how each structure can be constructed from the other, revealing new insights into combinatorial design theory.

Contribution

It establishes a bidirectional construction method linking finite projective planes and MPLS, providing a novel approach to understanding their equivalence and interdependence.

Findings

Finite projective planes of order k produce MPLS sets of order k.

Complete MPLS sets can be used to construct finite projective planes.

The paper demonstrates a reversible process between these combinatorial structures.

Abstract

We will see that every finite projective plane of order k > 1 gives rise to a complete set of (k-1) MPLS (= mutually projective latin squares) of order k and by reversing the process we can construct a finite projective plane of order k when a complete set of (k-1) MPLS of order k is given.