Discrepancy bounds for low-dimensional point sets
Abstract
The class of $(t,m,s)$-nets and $(t,s)$-sequences, introduced in their most general form by Niederreiter, are important examples of point sets and sequences that are commonly used in quasi-Monte Carlo algorithms for integration and approximation. Low-dimensional versions of $(t,m,s)$-nets and $(t,s)$-sequences, such as Hammersley point sets and van der Corput sequences, form important sub-classes, as they are interesting mathematical objects from a theoretical point of view, and simultaneously serve as examples that make it easier to understand the structural properties of $(t,m,s)$-nets and $(t,s)$-sequences in arbitrary dimension. For these reasons, a considerable number of papers have been written on the properties of low-dimensional nets and sequences.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2014
- DOI:
- 10.48550/arXiv.1407.0819
- arXiv:
- arXiv:1407.0819
- Bibcode:
- 2014arXiv1407.0819F
- Keywords:
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- Mathematics - Number Theory;
- 11K38;
- 11K06