On construction of strong orthogonal arrays and column-orthogonal strong orthogonal arrays of strength two plus

Computer experiments require space-filling designs with good low-dimensional projection properties. Strong orthogonal arrays are a type of space-filling design that provides better stratifications in low dimensions than ordinary orthogonal arrays. In this paper, we address the problem of constructing strong orthogonal arrays and column-orthogonal strong orthogonal arrays of strength two plus. Existing methods typically rely on regular designs or specific nonregular designs as base orthogonal arrays, limiting the sizes of the final designs. Instead, we propose two general methods that are easy to implement and applicable to a wide range of base orthogonal arrays. These methods produce space-filling designs that can accommodate a large number of factors, provide significant flexibility in terms of run sizes, and possess appealing low-dimensional projection properties. Therefore, these designs are ideal for computer experiments.