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1
Content available remote

Discrepancy and diaphony of digital (0,1)-sequences in prime base

100%
Faure H.
Acta Arithmetica
|
2005
|
tom 117
|
nr 2
125-148
2
Content available remote

Minoration de discrépance en dimension deux

64%
Faure H., Chaix H.
Acta Arithmetica
|
1996
|
tom 76
|
nr 2
149-164
3
Content available remote

Discrépance et diaphonie en dimension un

64%
Chaix H., Faure H.
Acta Arithmetica
|
1993
|
tom 63
|
nr 2
103-141
4
Content available remote

Irreducible Sobol' sequences in prime power bases

64%
Faure H., Lemieux C.
Acta Arithmetica
|
2016
|
tom 173
|
nr 1
59-80
EN
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 upper triangular matrices, and they have an easy-to-implement column-by-column construction. We prove they form a subfamily of the wide family of generalized Niederreiter sequences, hence satisfying all known discrepancy bounds for this family. Further, their connections with Niederreiter sequences show these two families only have a small intersection (after reordering the rows of generating matrices of Niederreiter sequences in that intersection).
5
Content available remote

Improvements on the star discrepancy of (t,s)-sequences

64%
Faure H., Lemieux C.
Acta Arithmetica
|
2012
|
tom 154
|
nr 1
61-78
6
Content available remote

A generalization of NUT digital (0,1)-sequences and best possible lower bounds for star discrepancy

64%
Faure H., Pillichshammer F.
Acta Arithmetica
|
2013
|
tom 158
|
nr 4
321-340
EN
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 of NUT digital (0,1)-sequences and to show in which sense Faure's formulas remain valid for this generalization. As an application we obtain best possible lower bounds for the star discrepancy of several subclasses of (0,1)-sequences.
7
Content available remote

Corrigendum to: "Improvements on the star discrepancy of (t,s)-sequences" (Acta Arith. 154 (2012), 61-78)

64%
Faure H., Lemieux C.
Acta Arithmetica
|
2013
|
tom 159
|
nr 3
299-300
EN
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.
8
Content available remote

L₂ discrepancy of generalized two-dimensional Hammersley point sets scrambled with arbitrary permutations

51%
Faure H., Pillichshammer F., Pirsic G., Schmid W.
Acta Arithmetica
|
2010
|
tom 141
|
nr 4
395-418
9
Content available remote

Discrépance de suites associées à un système de numération (en dimension s)

38%
Faure H.
Acta Arithmetica
|
1982
|
tom 41
|
nr 4
337-351
10
Content available remote

Discrépance quadratique de la suite de van der Corput et de sa symétrique

32%
Faure H.
Acta Arithmetica
|
1990
|
tom 55
|
nr 4
333-350
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