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

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.

DOI: 10.1090/S0025-5718-07-01984-9

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Cite this paper

@article{Dick2007TheCO, title={The construction of extensible polynomial lattice rules with small weighted star discrepancy}, author={Josef Dick}, journal={Math. Comput.}, year={2007}, volume={76}, pages={2077-2085} }