Bratley, Paul; Fox, Bennett L.; Niederreiter, Harald Implementation and tests of low-discrepancy sequences. (English) Zbl 0846.11044 ACM Trans. Model. Comput. Simul. 2, No. 3, 195-213 (1992). In recent years the concept of \((t,m,s)\)-nets and \((t,s)\)-sequences, introduced by Niederreiter, was investigated in great detail. These concepts provide point sets and sequences in the \(s\)-dimensional unit cube with extremely low discrepancy, and so they are of utmost importance for various quasi-Monte Carlo applications. A special example of \((t,s)\)-sequences of high quality are the so-called Niederreiter sequences. The present paper gives a short introduction into the concept of \((t,s)\)-sequences and of Niederreiter sequences. Further various methods for implementing the sequences are given, and finally an application by numerically integrating various test functions with the help of Niederreiter sequences is given. Reviewer: G.Larcher (Salzburg) Cited in 1 ReviewCited in 49 Documents MSC: 11K06 General theory of distribution modulo \(1\) 65D30 Numerical integration Keywords:quasi Monte Carlo integration; discrepancy; \((t,m,s)\)-nets; \((t,s)\)-sequences; Niederreiter sequences Software:Algorithm 647; TOMS659 PDFBibTeX XMLCite \textit{P. Bratley} et al., ACM Trans. Model. Comput. Simul. 2, No. 3, 195--213 (1992; Zbl 0846.11044) Full Text: DOI Link