10 papers
Asymptotically optimal bracketing covers for anchored boxes
Kosuke Suzuki
Bracketing covers and -covers provide finite discretizations of the anchored boxes that define the star discrepancy. Let and denote the corresponding b…
Separation properties of scrambled digital nets and related random point sets
Kosuke Suzuki
We study how standard randomization procedures affect the local geometry of quasi-Monte Carlo point sets, as measured by their minimum distance and mesh ratio. Although probabilist…
Coarse scrambling for Sobol' and Niederreiter sequences
Kosuke Suzuki
We introduce coarse scrambling, a novel randomization for digital sequences that permutes blocks of digits in a mixed-radix representation. This construction is designed to preserv…
Disproving the quasi-uniformity of the Halton sequences and of some Halton-type sequences
Takashi Goda, Roswitha Hofer, Kosuke Suzuki
In this short article, we prove that the Halton sequence, one of the most well-known low-discrepancy sequences, is not quasi-uniform in any dimension with any pairwise re…
On the quasi-uniformity properties of quasi-Monte Carlo point sets and sequences -- Part I: Lattices and Kronecker sequences
Josef Dick, Takashi Goda, Gerhard Larcher +2
The discrepancy of a point set quantifies how well the points are distributed, with low-discrepancy point sets demonstrating exceptional uniform distribution properties. Such sets…
On the quasi-uniformity properties of quasi-Monte Carlo point sets and sequences -- Part II: digital nets and sequences
Josef Dick, Takashi Goda, Kosuke Suzuki
We study the quasi-uniformity properties of digital nets, a class of quasi-Monte Carlo point sets. Quasi-uniformity is a space-filling property used for instance in experimental de…