Irregularities of distribution of digital -sequences in prime base.
Problème du cercle et harmoniques sphériques
Solution du problème 90
Lieu des intersections successives des ellipses ayant un diamètre donné de grandeur et de position et son conjugué donné de grandeur seulement
Discrépance quadratique de la suite de van der Corput et de sa symétrique
Discrépance de suites associées à un système de numération (en dimension s)
Discrépances de suites associées à un système de numération (en dimension un)
Van der Corput sequences towards general (0,1)–sequences in base b
As a result of recent studies on unidimensional low discrepancy sequences, we can assert that the original van der Corput sequences are the worst distributed with respect to various measures of irregularities of distribution among two large families of –sequences, and even among all –sequences for the star discrepancy . We show in the present paper that it is not the case for the extreme discrepancy by producing two kinds of sequences which are the worst distributed among all –sequences, with...
Discrepancy and diaphony of digital (0,1)-sequences in prime base
Discrépance de la suite de van der Corput
Discrépance et diaphonie en dimension un
Minoration de discrépance en dimension deux
Irreducible Sobol' sequences in prime power bases
Sobol' sequences are a popular family of low-discrepancy sequences, in spite of requiring primitive polynomials instead of irreducible ones in later constructions by Niederreiter and Tezuka. We introduce a generalization of Sobol' sequences that removes this shortcoming and that we believe has the potential of becoming useful for practical applications. Indeed, these sequences preserve two important properties of the original construction proposed by Sobol': their generating matrices are non-singular...
Improvements on the star discrepancy of (t,s)-sequences
Corrigendum to: "Improvements on the star discrepancy of (t,s)-sequences" (Acta Arith. 154 (2012), 61-78)
This short note is intended to correct an inaccuracy in the proof of Theorem 3 in the paper mentioned in the title. The result of Theorem 3 remains true without any other change in the proof. Furthermore, a misprint is pointed out.
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...
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...
L₂ discrepancy of generalized two-dimensional Hammersley point sets scrambled with arbitrary permutations
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