Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4648809 | Discrete Mathematics | 2011 | 25 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Jan Baldeaux, Josef Dick, Friedrich Pillichshammer,