A class of space-filling designs with low-dimensional stratification and column orthogonality

Strong orthogonal arrays are suitable designs for computer experiments because of stratification in low-dimensional projections. However, strong orthogonal arrays may be very expensive for a moderate number of factors. In this article, we develop a method for constructing space-filling designs with more economical run sizes. These designs are not only column-orthogonal but also enjoy a large proportion of low-dimensional stratification properties that strong orthogonal arrays ought to have. Moreover, a class of proposed designs can be 3-orthogonal. In addition, some theoretical results on regular fractional factorial designs are obtained as a by-product.