English

Discrepancy bounds for low-dimensional point sets

Number Theory 2014-07-04 v1

Abstract

The class of (t,m,s)(t,m,s)-nets and (t,s)(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)(t,m,s)-nets and (t,s)(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)(t,m,s)-nets and (t,s)(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.

Cite

@article{arxiv.1407.0819,
  title  = {Discrepancy bounds for low-dimensional point sets},
  author = {Henri Faure and Peter Kritzer},
  journal= {arXiv preprint arXiv:1407.0819},
  year   = {2014}
}
R2 v1 2026-06-22T04:54:08.854Z