On The Relationships Between Latin Squares, Finite Geometries & Balanced Incomplete Block Designs (BIBDs)

Abstract

In this project, we have reviewed the methods of constructing Balanced Incomplete Block Designs (BIBDs) by means of Mutually Orthogonal Latin squares (MOLS) of prime powers order arising from Finite Geometries and Finite Fields. This project nds that the existence of an A ne plane of prime powers order implies the existence of a set of Mutually Orthogonal Latin squares (MOLS) of the same order, a treatment square of side equal to the prime powers order, a set of bijective maps de ned on the key Latin square into the treatment space and a transformation de ned on the set of bijective maps that generates new sets of bijective maps that are the mappings of the remaining MOLS into the treatment square.