In the area of computer simulation, Latin hypercube designs play an important role. In this paper the classes of maximin and Audze-Eglais Latin hypercube designs are considered. Up to now only several two-dimensional designs and a few higher dimensional designs for these classes have been published. Using periodic designs and the Enhanced Stochastic Evolutionary algorithm of Jin et al. (J. Stat. Plan. Interference 134(1):268-687, 2005), we obtain new results which we compare to existing results. We thus construct a database of approximate maximin and Audze-Eglais Latin hypercube designs for up to ten dimensions and for up to 300 design points. All these designs can be downloaded from the website http://www.spacefillingdesigns.nl.

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The problem of finding a maximin Latin hypercube design in two dimensions can be described as positioning n nonattacking rooks on an n×n chessboard such that the minimal distance between pairs of rooks is maximized. Maximin Latin hypercube designs are important for the approximation and optimization of black-box functions. In this paper, general formulas are derived for maximin Latin hypercube designs for general n, when the distance measure is l or l 1. Furthermore, for the distance measure l 2 , we obtain maximin Latin hypercube designs for n 70 and approximate maximin Latin hypercube designs for other values of n. All these maximin Latin hypercube designs can be downloaded from the website http://www.spacefillingdesigns.nl. We show that the reduction in the maximin distance caused by imposing the Latin hypercube design structure is small. This justifies the use of maximin Latin hypercube designs instead of unrestricted designs.

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