A nested orthogonal array is an OA(N, k, s, g)which contains an OA(M, k, r, g) as a subarray. Here r < s andM<N . Necessary conditions for the existence of such arrays are obtained in the form of upper bounds on k, given N,M, s, r and g. Examples are given to show that these bounds are quite powerful in proving nonexistence. The link with incomplete orthogonal arrays is also indicated. © 2007 E...

(t,m, s)-nets are point sets in Euclidean s-space satisfying certain uniformity conditions, for use in numerical integration. They can be equivalently described in terms of ordered orthogonal arrays, a class of finite geometrical structures generalizing orthogonal arrays. This establishes a link between quasi-Monte Carlo methods and coding theory. In the present paper we prove an asymptotic Gil...

This paper attempts to explain the empirically demonstrated phenomena that, under some conditions, one-ata-time experiments outperform orthogonal arrays (on average) in parameter design of engineering systems. Five case studies are presented, each based on data from previously published full factorial experiments on actual engineering systems. Computer simulations of adaptive one-at-a-time plan...

The modular design of planar phased arrays arranged on orthogonal polygon-shaped apertures is addressed and a new method proposed to synthesize domino-tiled fitting multiple, generally conflicting, requirements. Starting from an analytic procedure check the domino-tileability aperture, two multi-objective optimization techniques are derived efficiently effectively deal with small medium/large d...

The quantum orthogonal arrays define remarkable classes of multipartite entangled states called $k$-uniform whose every reductions to $k$ parties are maximally mixed. We present constructions strength 2 with levels prime power, as well some 3. As a consequence, we give infinite 2-uniform $N$ systems dimension power $d\geq 2$ for arbitrary $N\geq 5$; 3-uniform $N$-qubit 6$ and $N\neq 7,8,9,11$; ...

When an orthogonal array is projected on a small number of factors, as is done in screening experiments, the question of interest is the structure of the projected design, by which we mean its decomposition in terms of smaller arrays of the same strength. In this paper we investigate the decomposition of arrays of strength t having t + 1 factors. The decomposition problem is well-understood for...

The problem of classifying all isomorphism classes of OA(N, k, s, t)s is shown to be equivalent to finding all isomorphism classes of non-negative integer solutions to a system of linear equations under the symmetry group of the system of equations. A branch-and-cut algorithm developed by Margot (2002, 2003a, 2003b, 2005) for solving integer programming problems with large symmetry groups is us...