5 papers · 1 filter
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…
Lower bounds on the discrepancy of digital NUT sequences
Ralph Kritzinger, Friedrich Pillichshammer
We study the discrepancy of digital NUT sequences which are an important sub-class of digital -sequences in the sense of Niederreiter. The main result is a lower bound…
Extremal Distributions of Discrepancy functions
Ralph Kritzinger, Markus Passenbrunner
The irregularities of a distribution of points in the unit interval are often measured with various notions of discrepancy. The discrepancy function can be defined with respect…
Digital nets in dimension two with the optimal order of discrepancy
Ralph Kritzinger, Friedrich Pillichshammer
We study the discrepancy of two-dimensional digital nets for finite . In the year 2001 Larcher and Pillichshammer identified a class of digital nets for which the symmetri…