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The Existence of Good Extensible Polynomial Lattice Rules

Abstract.

 Extensible (polynomial) lattice rules have been introduced recently and they are convenient tools for quasi-Monte Carlo integration. It is shown in this paper that for suitable infinite families of polynomial moduli there exist generating parameters for extensible rank-1 polynomial lattice rules such that for all these infinitely many moduli and all dimensions s the quantity R (s) and the star discrepancy are small. The case of Korobov-type polynomial lattice rules is also considered.

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Received April 30, 2002; in revised form August 21, 2002 Published online April 4, 2003

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Niederreiter, H. The Existence of Good Extensible Polynomial Lattice Rules. Monatsh. Math. 139, 295–307 (2003). https://doi.org/10.1007/s00605-002-0530-z

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  • DOI: https://doi.org/10.1007/s00605-002-0530-z

  • 2000 Mathematics Subject Classification: 11K45, 65C05, 65D30
  • Key words: Quasi-Monte Carlo methods, digital nets, lattice rules, polynomial lattice rules