A thorough analysis of the discrepancy of shifted Hammersley and van der Corput point sets

We study the star discrepancy of Hammersley nets and van der Corput sequences which are important examples of low-dimensional quasi-Monte Carlo point sets. By a so-called digital shift, the quality of distribution of these point sets can be improved. In this paper, we advance and extend existing bounds on digitally shifted Hammersley and van der Corput point sets and establish criteria for the choice of digital shifts leading to optimal results. Our investigations are partly based on a close analysis of certain sums of distances to the nearest integer.

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