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.