Some constructions of \((t,m,s)\)-nets with improved parameters
type: Item
instance of: scholarly article
title: Some constructions of \((t,m,s)\)-nets with improved parameters
zbMATH Open document ID: 1162.11041
author: San Ling
author: Ferruh Özbudak
published in: Finite Fields and their Applications
publication date: 2008-08-27T00:00:00Z
review text: Some digital \((t,m,s)\)-nets over \(\mathbb F_4\) are constructed for the following three cases: (1) \(t=m-4\), \(m=2f\), \(s=(2^{2f}-1)/3\), where \(f\geq 3\) is an integer; (2) \(t=m-4\), \(m=f\), \(s=(2^f+1)/3\), where \(f\geq 7\) is an odd integer; (3) \(t=m-4\), \(m=f+1\), \(s=(2^f+1)/3\), where \(f\geq 3\) is an odd integer. These constructions improve the best known parameters of \((t,m,s)\)-nets in [\textit{R. Schürer} and \textit{W. Ch. Schmid}, in: Niederreiter, Harald (ed.) et al., Monte Carlo and Quasi-Monte Carlo Methods 2004, Berlin: Springer, 457--469 (2006; Zbl 1130.65302)]. Furthermore, the authors also improve the bound for some parameters obtained by \textit{H. Niederreiter} and \textit{C. P. Xing} [Acta. Arith. 102, No. 2, 189--197 (2002; Zbl 0988.11032)] in the asymptotic theory of digital \((t,m,s)\)-nets.
Mathematics Subject Classification ID: 11K45
Mathematics Subject Classification ID: 11K31
Mathematics Subject Classification ID: 11T71
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 5316920
zbMATH Keywords: \((t,m,s)\)-net
zbMATH Keywords: digital net
zbMATH Keywords: finite field
zbMATH Keywords: linear code
reviewed by: Yaochen Zhu
describes a project that uses: MinT
MaRDI profile type: Publication
full work available at URL: j.ffa.2007.09.007
OpenAlex ID: W2027741940
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DOI: 10.1016/J.FFA.2007.09.007
description: scientific article; zbMATH DE number 5316920