Abstract: Space-filling designs with low-dimensional stratifications are desirable choices for computer experiments. In addition, column orthogonality is an important property of designs for such experiments, because it allows the estimates of the main effects in linear models to be uncorrelated with each other. However, few works have examined space-filling designs with both properties. This paper proposes a new class of designs called strong group-orthogonal arrays, the columns of which can be partitioned into groups, with the columns from different groups being column orthogonal and enjoying attractive low-dimensional stratifications. In addition, the overall arrays collapse to fully orthogonal arrays that accommodate large numbers of factors, making them particularly suitable for computer experiments. Methods for constructing this class of arrays based on both regular and nonregular designs are proposed. Difference schemes play a key role in the construction. Lastly, the proposed methods are easy to implement.

Key words and phrases: Column orthogonality, computer experiment, space-filling design, strong orthogonal array.