The Connection Between Finite Projective Planes And Latin Squares

Abstract

A Latin square arrangement is an arrangement of r symbols in r rows and c columns, such that every symbol occurs once in each row and each column. When two Latin squares of same order are superimposed on one another, in the resultant array if every ordered pair of symbols occurs exactly once, then the two Latin squares are said to be orthogonal. If in a set of Latin squares, any two Latin squares are orthogonal then the set is called Mutually Orthogonal Latin Squares of order r. Methods of constructing when p is prime or prime power are discussed here. A finite projective plane of order n exists if n is a prime or power of a prime number and it has been assumed that this is the only one that exists, reminiscent of the conjecture about the existence of  Latin squares n x n orthogonal to each other, so that these two existence problems are equivalent.