Some constructions of \((t,m,s)\)-nets with improved parameters
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.
scientific article; zbMATH DE number 5316920