Premium
Coding‐theoretic constructions for ( t , m , s )‐nets and ordered orthogonal arrays
Author(s) -
Bierbrauer Jürgen,
Edel Yves,
Schmid Wolfgang Ch.
Publication year - 2002
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.10015
Subject(s) - hamming space , mathematics , coding theory , combinatorics , hamming distance , hamming bound , concatenation (mathematics) , euclidean space , dimension (graph theory) , discrete mathematics , space (punctuation) , hamming code , hamming graph , block code , algorithm , computer science , decoding methods , operating system
( 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 +υ)‐construction and concatenation. We present a table of the best known parameters of q ‐ary ( t , m , s )‐nets for q ε{2,3,4,5} and dimension m ≤50. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 403–418, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10015