Orthogonal arrays and other combinatorial aspects in the theory of uniform point distributions in unit cubes
type: Item
instance of: scholarly article
title: Orthogonal arrays and other combinatorial aspects in the theory of uniform point distributions in unit cubes
zbMATH Open document ID: 0918.11045
DOI: 10.1016/0012-365X(92)90566-X
author: Harald Niederreiter
published in: Discrete Mathematics
publication date: 1993-01-16T00:00:00Z
review text: In [Monatsh. Math. 104, 273-337 (1987; Zbl 0626.10045)], the author introduced and gave various constructions for and properties of \((t,m,s)\)-nets. Such nets are of importance in the study of low-discrepancy point sets in \([0,1)^s, s\geq 2.\) Such nets were shown to be related to various combinatorial structures, for example to sets of mutually orthogonal latin squares. \textit{G. L. Mullen} and \textit{G. Whittle} [Monatsh. Math. 113, 265-273 (1972; Zbl 0765.11032)], extended this equivalence via sets of orthogonal hypercubes of higher dimensions. In this note the author shows the equivalence of certain \((t,m,s)\)-nets to orthogonal arrays. He also discusses a combinatorial problem for vector spaces over finite fields which generalizes a problem from algebraic coding theory, namely that of determining the largest minimum distance which can be achieved by a linear code over a finite field with given length and dimension.
reviewed by: Gary L. Mullen
Mathematics Subject Classification ID: 11K38
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 94543
zbMATH Keywords: orthogonal arrays
zbMATH Keywords: uniform distribution
zbMATH Keywords: minimum distance
zbMATH Keywords: linear code over finite field
zbMATH Keywords: (t,m,s)-nets
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 94543