Two-dimensional minimax Latin hypercube designs

Authors:
Edwin R. van Dam
Affiliations:
Tilburg University, Department of Econometrics and O.R., PO Box 90153, 5000 LE Tilburg, The Netherlands
Venue:
Discrete Applied Mathematics
Year:
2008

Citing 4
Cited 1

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Abstract

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.