Constructions of column-orthogonal strong orthogonal arrays via matchings of bipartite graphs

Strong orthogonal arrays (SOAs) have better space-filling properties than ordinary orthogonal arrays for computer experiments. SOAs of strengths two plus and two star can improve the space-filling properties in low dimensions, and column orthogonality plays a vital role in computer experiments. In this paper, we use matchings of the bipartite graphs and Hall’s theorem to present several constructions of column-orthogonal SOAs of strengths two plus and two star. We also give a new direct construction of SOAs of strength two plus. Our constructions can provide larger numbers of factors of SOAs and column-orthogonal SOAs of strengths two plus and two star than those in the existing literature, having flexible run sizes. The constructions are convenient and flexible, and the resulting designs are good for computer experiments.