Discrepancy of Hyperplane Nets and Cyclic Nets

Digital nets are very important representatives in the family of low-discrepancy point sets which are often used as underlying nodes for quasi-Monte Carlo integration rules. Here we consider a special sub-class of digital nets known as cyclic nets and, more general, hyperplane nets. We show the existence of such digital nets of good quality with respect to star discrepancy in the classical as well as weighted case and we present effective search algorithms based on a component-by-component construction.

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