Constructing Orthogonal Arrays on Non-abelian Groups

Abstract

For an orthogonal array (or fractional factorial design) on k factors, Xu and Wu (2001) define the array's generalized wordlength pattern (A1, ..., Ak), by relating a cyclic group to each factor. They prove the property that the array has strength t if and only if A1 = ... = At = 0. In their 2012 paper, Beder and Beder show that this result is independent of the group structure used. Non-abelian groups can be used if the assumption is made that the groups Gi are chosen so that the counting function O of the array is a class function on G. The aim of this thesis is to construct examples of orthogonal arrays on G = G1 x ... x Gk, where G is non-abelian, having two properties: given strength, and counting function O that is constant on the conjugacy classes of G.