Two-Dimensional Minimax Latin Hypercube Designs

We investigate minimax Latin hypercube designs in two dimensions for several distance measures.For the l-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 l1-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 l2-distance we have generated minimax solutions up to n = 27 by an exhaustive search method.The latter Latin hypercube designs will be included in the website www.spacefillingdesigns.nl.