Association Schemes for Ordered Orthogonal Arrays and (t,m,s)-nets

Linear Programming Bounds for Ordered Orthogonal Arrays and (T;M;S)-nets

A recent theorem of Schmid and Lawrence establishes an equivalence between (T; M; S)-nets and ordered orthogonal arrays. This leads naturally to a search both for constructions and for bounds on the size of an ordered orthogonal array. Subsequently, Martin and Stinson used the theory of association schemes to derive such a bound via linear programming. In practice, this involves large-scale com...

A Generalized Rao Bound for Ordered Orthogonal Arrays and (t; M; S)-nets

In this paper, we provide a generalization of the classical Rao bound for orthogonal arrays, which can be applied to ordered orthogonal arrays and (t; m; s)-nets. Application of our new bound leads to improvements in many parameter situations to the strongest bounds (i.e., necessary conditions) for existence of these objects.

Geometrical Constructions for Ordered Orthogonal Arrays and (T, M, S)-Nets

The concept of a linear ordered orthogonal array is introduced, and its equivalent geometrical configuration is determined when its strength is 3 and 4. Existence of such geometrical configurations is investigated. They are also useful in the study of (T, M, S)-nets.

Linear programming bounds for (T,M, S)-nets

of volume bT−M contains exactly b points of the net. (Note that V ol(E) = b− ∑ di .) These deterministic low-discrepancy point sets have proven powerful in the estimate of high-dimensional integrals. The goal is to make the quality parameter T as close to zero as possible. Some researchers work on constructions of such nets and ideas from coding theory have led to very powerful examples [7]. Bu...

Coding-theoretic constructions for (t,m, s)-nets and ordered orthogonal arrays