PERMUTATION GROUPS AND INTEGER LINEAR ALGEBRA FOR ENUMERATION OF ORTHOGONAL ARRAYS

Abstract

We introduce new group theoretic methods for constructing mixed orthogonal arrays (OAs). In brief, we employ combinatorics, graph and permutation group theory, together with integer linear formulation as major engines to provide a framework for constructing and enumerating mixed OAs of any strength with all feasible factor levels and with run sizes satisfying the Rao bound. The proposed methods are validated by constructing a few new strength 3 mixed OAs with run sizes at most 100.