A randomly generated Latin hypercube design (LHD) can be quite structured: the variables may be highly correlated or the design may not have good space-filling properties. There are procedures for finding good LHDs by minimizing the pairwise correlations or by maximizing the inter-site distances. In this article we show that these two criteria need not be in close agreement. We propose a multi-...

In [5] Raghavarao showed that if n = 2 (mod 4) and A is a {O, 1, -1} matrix satisfying AAt = (n 1) In. then n 1 = a2 b2 for a, b integers. In [4] van Lint and Seidel giving a proof modeled on a proof of the Witt cancellation theorem, proved more generally that if n is as above and A is a rational matrix satisfying AAt = kIn then k = q12 + q22 (q1, q2 E Q, the rational numbers). Consequently, if...

We study the use of negacyclic matrices to form orthogonal designs and hence Hadamard matrices. We give results for all possible tuple for order 12, all but 3 for order 20 and all but 3 for order 28.

We propose several methods for constructing nested (nearly) orthogonal designs intended for multi-fidelity computer experiments. Such designs are two (nearly) orthogonal designs with one nested within the other. Our methods exploit nesting in such discrete structures as fractional factorial designs, Hadamard matrices, and rotation matrices. Examples are given illustrating the proposed methods.