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# Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

Editorial Board: Binder, Kurt / Bouleau, Nicolas / Chorin, Alexandre J. / Dimov, Ivan / Dubus, Alain / Egorov, Alexander D. / Ermakov, Sergei M. / Halton, John H. / Heinrich, Stefan / Kalos, Malvin H. / Lepingle, D. / Makarov, Roman / Mascagni, Michael / Mathe, Peter / Niederreiter, Harald / Platen, Eckhard / Sawford, Brian R. / Schmid, Wolfgang Ch. / Schoenmakers, John / Simonov, Nikolai A. / Sobol, Ilya M. / Spanier, Jerry / Talay, Denis

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Volume 22, Issue 4

# A search for extensible low-WAFOM point sets

Shin Harase
• Corresponding author
• College of Science and Engineering, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga, 525-8577, Japan
• Email
• Other articles by this author:
Published Online: 2016-11-19 | DOI: https://doi.org/10.1515/mcma-2016-0119

## Abstract

Matsumoto, Saito and Matoba recently proposed the Walsh figure of merit (WAFOM), which is a computable criterion for quasi-Monte Carlo point sets using digital nets. Several algorithms have been proposed for finding low-WAFOM point sets. In the existing algorithms, the number of points is fixed in advance, but extensible point sets are preferred in some applications. In this paper, we propose a random search algorithm for extensible low-WAFOM point sets. For this, we introduce a method that uses lookup tables to compute WAFOM faster. Numerical results show that our extensible low-WAFOM point sets are comparable with Niederreiter–Xing sequences for some low-dimensional and smooth test functions.

MSC 2010: 65C05; 65D30; 65C10; 11K45

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Accepted: 2016-11-11

Published Online: 2016-11-19

Published in Print: 2016-12-01

Funding Source: Japan Society for the Promotion of Science

Award identifier / Grant number: 26730015

Award identifier / Grant number: 24.7985

Award identifier / Grant number: 26310211

Award identifier / Grant number: 15K13460

The author was partially supported by the Grants-in-Aid for Young Scientists (B) #26730015, for JSPS Fellows 247985, for Scientific Research (B) 26310211, and for Challenging Exploratory Research #15K13460 from the Japan Society for the Promotion of Scientific Research.

Citation Information: Monte Carlo Methods and Applications, Volume 22, Issue 4, Pages 349–357, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629,

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