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The number of lattice rules having given invariants

Published online by Cambridge University Press:  17 April 2009

Stephen Joe  and
David C. Hunt
Stephen Joe
Affiliation:
Department of Mathematics and Statistics, The University of Waikato, Hamilton, New Zealand
David C. Hunt
Affiliation:
School of Mathematics, University of New South Wales, Sydney NSW 2033, Australia
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Abstract

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A lattice rule is a quadrature rule used for the approximation of integrals over the s-dimensional unit cube. Every lattice rule may be characterised by an integer r called the rank of the rule and a set of r positive integers called the invariants. By exploiting the group-theoretic structure of lattice rules we determine the number of distinct lattice rules having given invariants. Some numerical results supporting the theoretical results are included. These numerical results are obtained by calculating the Smith normal form of certain integer matrices.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 46 , Issue 3 , December 1992 , pp. 479 - 495
Copyright
Copyright © Australian Mathematical Society 1992

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