We construct infinite-dimensional highly-uniform point sets for quasi- Monte Carlo integration. The successive coordinates of each point are determined by a linear recurrence in F2w , the finite field with 2w elements where w is an inte- ger, and a mapping from this field to the interval [0, 1). One interesting property of these point sets is that almost all of their two-dimensional projections are perfectly equidistributed. We performed searches for specific parameters in terms of differ- ent measures of uniformity and different numbers of points. We give a numerical illustration showing that using randomized versions of these point sets in place of independent random points can reduce the variance drastically for certain functions.
CITATION STYLE
Panneton, F., & L’Ecuyer, P. (2006). Infinite-Dimensional Highly-Uniform Point Sets Defined via Linear Recurrences in $$\mathbb{F}_{2^w } $$. In Monte Carlo and Quasi-Monte Carlo Methods 2004 (pp. 419–429). Springer-Verlag. https://doi.org/10.1007/3-540-31186-6_25
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