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Duality theory and propagation rules for higher order nets. (English) Zbl 1229.11103
The higher order nets and sequences are used in quasi-Monte Carlo rules for accurately evaluating high dimensional integrals of smooth functions.
This paper introduces a duality theory for higher order nets whose construction is not necessarily based on linear algebra over finite fields. Furthermore, this paper proves propagation rules which show how to obtain new higher order nets and sequences from existing ones and how the parameters of these point sets propagate under these rules.

MSC:
11K45 Pseudo-random numbers; Monte Carlo methods
11K36 Well-distributed sequences and other variations
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