Coding-theoretic constructions for (t,m,s)-nets and ordered orthogonal arrays
Document Type
Article
Publication Date
10-7-2002
Department
Department of Mathematical Sciences
Abstract
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.
Publication Title
Journal of Combinatorial Designs
Recommended Citation
Bierbrauer, J.,
Edel, Y.,
&
Schmid, W.
(2002).
Coding-theoretic constructions for (t,m,s)-nets and ordered orthogonal arrays.
Journal of Combinatorial Designs,
10(6), 403-418.
http://doi.org/10.1002/jcd.10015
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/3704
Publisher's Statement
© 2002 Wiley Periodicals, Inc. Publisher’s version of record: https://doi.org/10.1002/jcd.10015