A note on the figure of merit of 2-dimensional rank 2 lattice rules.
Improvements of the discrepancy of the van der Corput sequence.
Dyadic diaphony of digital sequences
The dyadic diaphony is a quantitative measure for the irregularity of distribution of a sequence in the unit cube. In this paper we give formulae for the dyadic diaphony of digital -sequences over , . These formulae show that for fixed , the dyadic diaphony has the same values for any digital -sequence. For , it follows that the dyadic diaphony and the diaphony of special digital -sequences are up to a constant the same. We give the exact asymptotic order of the dyadic diaphony of digital...
Improved upper bounds for the star discrepancy of digital nets in dimension 3
A generalization of NUT digital (0,1)-sequences and best possible lower bounds for star discrepancy
In uniform distribution theory, discrepancy is a quantitative measure for the irregularity of distribution of a sequence modulo one. At the moment the concept of digital (t,s)-sequences as introduced by Niederreiter provides the most powerful constructions of s-dimensional sequences with low discrepancy. In one dimension, recently Faure proved exact formulas for different notions of discrepancy for the subclass of NUT digital (0,1)-sequences. It is the aim of this paper to generalize the concept...
Optimal 𝓛₂ discrepancy bounds for higher order digital sequences over the finite field 𝔽₂
On the mean square weighted ℒ₂ discrepancy of randomized digital (t,m,s)-nets over ℤ₂
discrepancy of generalized Zaremba point sets
We give an exact formula for the discrepancy of a class of generalized two-dimensional Hammersley point sets in base , namely generalized Zaremba point sets. These point sets are digitally shifted Hammersley point sets with an arbitrary number of different digital shifts in base . The Zaremba point set introduced by White in 1975 is the special case where the shifts are taken repeatedly in sequential order, hence needing at least points to obtain the optimal order of discrepancy. On the...
Points sets with low discrepancy
Distribution properties of sequences generated by Q-additive functions with respect to Cantor representation of integers
L₂ discrepancy of generalized two-dimensional Hammersley point sets scrambled with arbitrary permutations
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