Search

Maximin distance designs and orthogonal designs have become increasingly popular in computer and physical experiments. The construction of such designs is challenging, especially under the maximin distance criterion. This paper studies a class of Latin hypercube designs by calculating the minimum distances between design points. We derive a general formula for the minimum intersite distance of this kind of design. The row pairs with the minimum intersite distance are also specified. The results show that such kind of Latin hypercube design is asymptotically optimal under both the maximin distance criterion and the orthogonality criterion. [ABSTRACT FROM AUTHOR]

Latin hypercube designs have found wide application in computer experiments. A number of methods have recently been proposed to construct orthogonal Latin hypercube designs. In this paper, we propose an approach for expanding the orthogonal Latin hypercube design in Sun et al. (Biometrika 96:971-974, ) to a nearly orthogonal Latin hypercube design of a larger column size. The newly added part has half number of columns of the original part. It can be shown that the upper bound of the maximum correlation between any two distinct columns of the resulting design is very small. Our method also works for expanding any symmetric Latin hypercube designs. [ABSTRACT FROM AUTHOR]