New bounds and search for maximin distance U-type designs

Maximin distance designs have attracted increasing attention in computer experiments owing to their appealing space-filling properties. The quality of these designs is typically evaluated by comparing their separation distance with the associated upper bound. Nevertheless, deriving tight upper bounds for the separation distance of designs remains a challenging problem that has been infrequently addressed in the literature. In this study, we obtain a new upper bound for the separation distance of certain classes of five-level U-type designs. We also investigate the characteristics of maximin distance U-type designs and show the optimality of some existing orthogonal designs. Based on these theoretical results, we develop an efficient algorithm for searching maximin distance U-type designs. Numerical studies and comparisons are given to show the superior performance of the obtained designs.