58 citations · 157 across the 61 of their papers we have counts for
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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…
Lebesgue constants for the Walsh system and the discrepancy of the van der Corput sequence
Josef Dick, Friedrich Pillichshammer
In this short note we report on a coincidence of two mathematical quantities that, at first glance, have little to do with each other. On the one hand, there are the Lebesgue const…
The BMO-discrepancy suffers from the curse of dimensionality
Friedrich Pillichshammer
We show that the minimal discrepancy of a point set in the -dimensional unit cube with respect to the BMO seminorm suffers from the curse of dimensionality.
Optimal periodic -discrepancy and diaphony bounds for higher order digital sequences
Friedrich Pillichshammer
We present an explicit construction of infinite sequences of points in the -dimensional unit-cube whose periodic…
Exact order of extreme discrepancy of infinite sequences in arbitrary dimension
Ralph Kritzinger, Friedrich Pillichshammer
We study the extreme discrepancy of infinite sequences in the -dimensional unit cube, which uses arbitrary sub-intervals of the unit cube as test sets. This is in contrast…
Point sets with optimal order of extreme and periodic discrepancy
Ralph Kritzinger, Friedrich Pillichshammer
We study the extreme and the periodic discrepancy of point sets in the -dimensional unit cube. The extreme discrepancy uses arbitrary sub-intervals of the unit cube as tes…