Mutually orthogonal latin squares based on Z 3x Z 9

by Carter, James Michael

This paper will investigate the number of mutually orthogonal latin squares, MOLS, that can be constructed using elements from the group G = Z 3× Z 9. In calculating this number, it is necessary to consider the group under the action of the homomorphism f : G ? K defined by f ((g 1, g 2))=(g 1mod 3, g 2mod 3) so that K = Im(G) is isomorphic to Z 3× Z 3, so that the action of f is to create the quotient group K = G/(0, 3). Based on data from the group Z 2× Z 4, the elements of the image should be permuted and constants added before considering G=f -1(K). The use of orthomorphisms will allow for the construction of orthogonal latin squares.