A characterization of strong orthogonal arrays of strength three

TL;DR

This paper provides a new, simplified characterization of strong orthogonal arrays of strength three using semi-embeddability, enhancing understanding and enabling construction of specific arrays.

Contribution

It introduces a direct and insightful characterization method for strong orthogonal arrays of strength three, advancing the theoretical framework and construction techniques.

Findings

New characterization via semi-embeddability

Simpler understanding of strong orthogonal arrays

Construction of two specific SOA(54,5,27,3) arrays

Abstract

In an early paper, He and Tang [Biometrika 100 (2013) 254-260] introduced and studied a new class of designs, strong orthogonal arrays, for computer experiments, and characterized such arrays through generalized orthogonal arrays. The current paper presents a simple characterization for strong orthogonal arrays of strength three. Besides being simple, this new characterization through a notion of semi-embeddability is more direct and penetrating in terms of revealing the structure of strong orthogonal arrays. Some other results on strong orthogonal arrays of strength three are also obtained along the way, and in particular, two $\operatorname {SOA}(54,5,27,3)$'s are constructed.