R package: Low WAFOM Sequences based on Niederreiter-Xing sequences

Low WAFOM Sequences based on Niederreiter-Xing sequences are searched using an algorithm described in Shinsuke Mori's Master's thesis.

Caution

Currently, this project is very experimental.

Link

• GitHub Page
• Project Page

Reference

• Shinsuke Mori, "Suuchi Sekibun no tameno QMC Ten Shuugou no Sekkei, Tansaku, oyobi sono Yuukousei", Master's Thesis, 2017.
• Ryuichi Ohori, "Efficient Quasi Monte Carlo Integration by Adjusting the Derivation-sensitivity Parameter of Walsh Figure of Merit", Master's Thesis, 2015.
• S. Harase and R. Ohori, "A search for extensible low-WAFOM point sets", arXiv preprint, arXiv:1309.7828, (2013), https://arxiv.org/abs/1309.7828.
• M. Matsumoto and R. Ohori, "Walsh Figure of Merit for Digital Nets: An Easy Measure for Higher Order Convergent QMC", Springer International Publishing, Cham, 2016, pp. 143-160.
• M. Matsumoto, M. Saito, and K. Matoba, "A computable figure of merit for quasi-Monte Carlo point sets", Mathematics of Computation, 83 (2014), pp. 1233-1250.
• G. Pirsic, "A software implementation of Niederreiter-Xing sequences", in Monte Carlo and Quasi-Monte Carlo Methods 2000, Springer, 2002, pp. 434-445. https://sites.google.com/site/isabelpirsic/nxlegacy.
• C. P. Xing and H. Niederreiter, "A construction of low-discrepancy sequences using global function fields", ACTA ARITHMETICA, 73 (1995), pp. 87-102.