Two-dimensional minimax Latin hypercube designs

We investigate minimax Latin hypercube designs in two dimensions for several distance measures. For the `-distance we are able to construct minimax Latin hypercube designs of n points, and to determine the minimal covering radius, for all n. For the `1-distance we have a lower bound for the covering radius, and a construction of minimax Latin hypercube designs for (infinitely) many values of n. We conjecture that the obtained lower bound is attained, except for a few small (known) values of n. For the `2-distance we have generated minimax solutions up to n = 27 by an exhaustive search method. The latter Latin hypercube designs are included in the website www.spacefillingdesigns.nl. c © 2008 Elsevier B.V. All rights reserved.