Selecting strong orthogonal arrays by linear allowable level permutations

Abstract

Space-filling designs are widely used in physical and computer experiments when the model between the response and input factors is uncertain. Recently, Chen and Tang (2022, Ann. Statist. 50, 2925–2949) justified the use of strong orthogonal arrays (SOAs) under a broad class of space-filling criteria. However, when allowable level permutations are applied to an SOA, a class of SOAs can be obtained with different geometrical structures and it is not clear which one should be selected for practical use. In this paper, we address this issue by considering a representative subset of allowable level permutations, called linear allowable level permutations. These special level permutations offer theoretical convenience in classifying various geometrically non-isomorphic SOAs. Based on these results, construction methods are provided to obtain SOAs that are more space-filling than those in the literature.