Construction Algorithms for Good Extensible Lattice Rules

Extensible (polynomial) lattice rules have the property that the number N of points in the node set may be increased while retaining the existing points. It was shown by Hickernell and Niederreiter in a nonconstructive manner that there exist generating vectors for extensible integration lattices of excellent quality for N=b,b2,b3,…, where b is a given integer greater than 1. Similar results were proved by Niederreiter for polynomial lattices. In this paper we provide construction algorithms for good extensible lattice rules. We treat the classical as well as the polynomial case.

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