A (symmetric) nested orthogonal array is a symmetric orthogonal array OA(N, k, s, g) which contains an OA(M,k, r, g) as a subarray, where M < N and r < s. In this communication, some methods of construction of nested symmetric orthogonal arrays are given. Asymmetric nested orthogonal arrays are defined and a few methods of their construction are described.

Nested orthogonal arrays are useful in obtaining space-filling designs for an experimental set up consisting of two experiments, the expensive one of higher accuracy to be nested in a larger inexpensive one of lower accuracy. Systematic construction methods of some families of symmetric and asymmetric nested orthogonal arrays were provided recently by Dey [Discrete Math. 310 (2010), 2831–2834]....

In this paper, we propose a new general approach to construct asymmetrical orthogonal arrays, namely generalized Kronecker product. The operation is not usual Kronecker product in the theory of matrices, but it is interesting since the interaction of two columns of asymmetrical orthogonal arrays can be often written out by the generalized Kronecker product. As an application of the method, some...

Orthogonal arrays (OAs) are basic combinatorial structures, originally studied by statisticians motivated by their applications to design of experiments. In recent years, they have found numerous applications in computer science. Among their applications are derandomization of algorithms, random pattern testing of VLSI chips, authentication codes, universal hash functions, threshold schemes, an...