Discrepancy of Hyperplane Nets and Cyclic Nets

Friedrich Pillichshammer () and Gottlieb Pirsic ()
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Friedrich Pillichshammer: Universität Linz, Institut für Finanzmathematik

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2008, 2009, pp 573-587 from Springer

Abstract: Abstract 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.

Keywords: Star Discrepancy; Weighted Case; Lattice Rule; Walsh Function; Polynomial Lattice (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-04107-5_37

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DOI: 10.1007/978-3-642-04107-5_37

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