Geometrical Constructions 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...

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...

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

In an earlier paper 9], we studied a generalized Rao bound for ordered orthogonal arrays and (T; M; S)-nets. In this paper, we extend this to a coding-theoretic approach to ordered orthogonal arrays. Using a certain association scheme, we prove a MacWilliams-type theorem for linear ordered orthogonal arrays and linear ordered codes as well as a linear programming bound for the general case. We ...

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.