An Equivalence between (T, M, S)-Nets and Strongly Orthogonal Hypercubes

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.

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.

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

An Asymptotic Gilbert - Varshamov Bound for ( T , M , S ) - Nets

(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...

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...