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Mathematics of Computation

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The construction of extensible polynomial lattice rules with small weighted star discrepancy

Author: Josef Dick
Journal: Math. Comp. 76 (2007), 2077-2085
MSC (2000): Primary 11K45, 65C05, 65D30
Published electronically: May 9, 2007
MathSciNet review: 2336283
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Abstract: In this paper we introduce a construction algorithm for extensible polynomial lattice rules and we prove that the construction algorithm yields generating vectors of polynomials which are optimal for a range of moduli chosen in advance. The construction algorithm uses a sieve where the generating vectors are extended by one coefficient in each component at each step and where one keeps a certain number of good ones and discards the rest. We also show that the construction can be done component by component.

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Additional Information

Josef Dick
Affiliation: School of Mathematics, University of New South Wales, Sydney 2052, Australia
Address at time of publication: UNSW Asia, 1 Kay Siang Road, Singapore 248922

Received by editor(s): April 19, 2006
Received by editor(s) in revised form: September 13, 2006
Published electronically: May 9, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.