Infinite-Dimensional Highly-Uniform Point Sets Defined via Linear Recurrences
in F_{2^w}
mcqmc04-f2w.pdf, F. Panneton and Pierre L’Ecuyer.
"Infinite-Dimensional Highly-Uniform Point Sets Defined via Linear Recurrences
in F_{2^w}", submitted for publication in the proceedings of the MC2QMC
2004 Conference.
Abstract:
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 F_{2^w}, the finite field with 2^w elements where
w is an integer, 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 different 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.