Abstract: Maximin distance designs are a kind of space-filling design, and are widely used in computer experiments. However, although much work has been done on constructing such designs, doing so for a large number of rows and columns remains challenging. In this paper, we propose a theoretical construction method that generates a maximin L₁-distance Latin hypercube design with a run size that is close to the number of columns, or half the number of columns. Our theoretical results show that some of the constructed designs are both maximin L₁-distance and equidistant designs, which means that their pairwise L₁-distances are all equal, and that they are uniform projection designs. Other designs are asymptotically optimal under the maximin L₁-distance criterion. Moreover, the proposed method is efficient for constructing high-dimensional Latin hypercube designs that perform well under the maximin L₁-distance criterion.

Key words and phrases: Computer experiment, Latin square, maximin distance design, space-filling design.