aSchool of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia;bInstitut für Finanzmathematik, Universität Linz, Altenbergstraße 69, A-4040 Linz, Austria
Abstract:
Higher order nets and sequences are used in quasi-Monte Carlo rules for the approximation of high dimensional integrals over the unit cube. Hence one wants to have higher order nets and sequences of high quality.In this paper we introduce a duality theory for higher order nets whose construction is not necessarily based on linear algebra over finite fields. We use this duality theory to prove propagation rules for such nets. This way we can obtain new higher order nets (sometimes with improved quality) from existing ones. We also extend our approach to the construction of higher order sequences.