×

Implementation and tests of low-discrepancy sequences. (English) Zbl 0846.11044

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.

MSC:

11K06 General theory of distribution modulo \(1\)
65D30 Numerical integration
PDFBibTeX XMLCite
Full Text: DOI Link