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

Abstract: (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. The ambient space is a metric space generalizing the Hamming space of coding theory.We denote it by NRT space (named after Niederreiter, Rosenbloom and Tsfasman). Our main results are generalizations of coding-theoretic constructions from Hamming space to NRT space. These comprise a version of the Gilbert-Varshamov bound, the (u; u v)-construction and concatenation. We present a table of the best known parameters of q-ary ot;m; s-nets for q 2 f2; 3; 4; 5g and dimension m 50. © 2002 Wiley Periodicals, Inc.