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