Construction of group strong orthogonal arrays of strength two plus

Strong orthogonal arrays (SOAs) have received more and more attention recently since they enjoy more desirable space-filling properties than ordinary orthogonal arrays. Among them, the SOAs of strength 2+ are the most advisable as they satisfy the same two-dimensional space-filling property as SOAs of strength 3 while having more columns for given run sizes. In addition, column-orthogonality is also a desirable property for designs of computer experiments. Existing column-orthogonal SOAs of strength 2+ have limited columns. In this paper, we propose a new class of space-filling designs, called group SOAs of strength 2+ , and provide construction methods for such designs. The proposed designs can accommodate more columns than column-orthogonal SOAs of strength 2+ for given run sizes while satisfying similar stratifications and retaining a high proportion of column-orthogonal columns. Orthogonal arrays and difference schemes play important roles in the construction. The construction procedures are easy to implement and a large amount of group SOAs with s^2 levels are constructed where s ≥ 2 is a prime power. In addition, the run sizes of the constructed designs are s times the ones of the orthogonal arrays used in the construction procedure. Thus they are relatively flexible.