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.