Column-orthogonal strong orthogonal arrays and sliced strong orthogonal arrays

A strong orthogonal array of strength t can achieve uniformity on finer grids when projected onto any g dimensions for any g less than t. It can be regarded as a kind of uniform space-filling design. Meanwhile, orthogonality is also desir- able for space-filling designs. In this paper, we construct strong orthogonal arrays through ordinary orthogonal arrays, in a different fashion than do He and Tang (2013). The resulting strong orthogonal arrays have comparable columns with that of He and Tang (2013), and can achieve near or exact column-orthogonality in most cases, and even 3-orthogonality when the ordinary orthogonal arrays have strength no less than three. On the other hand, sliced space-filling designs are very useful for computer experiments with both qualitative and quantitative factors, multiple computer experiments, data pooling, and cross-validation procedures. Employing the good space-filling property of strong orthogonal arrays, we further propose a new kind of sliced space-filling design, called the sliced strong orthogonal array, and provide two methods for constructing designs for which the resulting designs and their slices also perform well in terms of both column-orthogonality and 3- orthogonality.