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arXiv · 1407.0819

Discrepancy bounds for low-dimensional point sets

Henri Faure·Peter Kritzer
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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.

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Henri Faure, Peter Kritzer. 2014-07-03. Discrepancy bounds for low-dimensional point sets. https://arxiv.org/abs/1407.0819

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