Construction of Generalized Minimum Aberration Three-Level Orthogonal Arrays with Three, Four and Five Columns

Abstract

In this paper, we construct generalized minimum aberration (GMA) three-level orthogonal arrays with three and four columns for any run size $$n \equiv $$ 0 (mod 9) and GMA three-level orthogonal arrays with five columns for $$n \equiv $$ 0, 18, 36, 81, 162, 207 and 225 (mod 243) runs. Efficient three-level orthogonal arrays with five columns are also constructed for $$n \equiv $$ 99, 117, 180 and 198 (mod 243) runs. All constructed GMA designs produce GMA designs when projected onto lower dimensions. Moreover, they possess a minimum confounding structure when the linear-quadratic system of contrasts is used for modeling the response.