A Construction Method for Maximin L1-Distance Latin Hypercube Designs

Abstract

Maximin distance designs are a kind of space-filling designs, which are widely used in computer experiments. A lot of work has been done for constructing such designs. Even so, construction of maximin distance designs with large row and column sizes is still challenging. In this paper, we propose a theoretical construction method for generating maximin L1-distance Latin hypercube designs whose run sizes are close to the number of columns or half of the number of columns. 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 they are also uniform projection designs; while others 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.