Oracle arrays and their use for constructing space-filling designs

Abstract The maximin distance is an attractive criterion for constructing space-filling designs. As factors in computer experiments are generally quantitative, the Lp-distance is appropriate. Theoretical construction of maximin Lp-distance designs, however, is extremely challenging. Given that directly attacking the problem is difficult, we propose an indirect approach that first constructs maximin Hamming distance designs and then constructs maximin Lp-distance designs using the former. The approach turns out to be very fruitful. We introduce oracle arrays, which are a special class of maximin Hamming distance arrays that also allow other maximin Hamming distance arrays to be easily constructed. We then examine how to use oracle arrays to construct maximin Lp-distance designs. Although the approach is motivated by the desire of constructing maximin Lp-distance designs, it can also be thought of as a generalization of the idea of orthogonal array based designs.