Discrepancy bounds for low-dimensional point sets
Number Theory
2014-07-04 v1
Abstract
The class of -nets and -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 -nets and -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 -nets and -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}
}