Construction of strong orthogonal arrays of strength three and three minus via Addelman–Kempthorne orthogonal arrays

Space-filling designs with superior low-dimensional properties are highly required in computer experiments. Strong orthogonal arrays (SOAs) represent a class of such designs that outperform ordinary orthogonal arrays in their stratification properties within low dimensions. Nevertheless, current methods for constructing high-strength SOAs are rare, and they typically rely on regular designs, thereby limiting the number of runs in the final arrays to prime powers. This study presents new construction methods for three types of SOAs: SOAs of strength three, column-orthogonal SOAs (OSOAs) of strength three and three minus. The resulting designs have run sizes of twice an odd prime power without replications, filling the gaps in run sizes left by existing constructions. The projection properties of Addelman–Kempthorne orthogonal arrays are instrumental in the development of these construction methods.