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

Henri Faure, and Friedrich Pillichshammer. "A generalization of NUT digital (0,1)-sequences and best possible lower bounds for star discrepancy." Acta Arithmetica 158.4 (2013): 321-340. <http://eudml.org/doc/278911>.

@article{HenriFaure2013,
abstract = {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.},
author = {Henri Faure, Friedrich Pillichshammer},
journal = {Acta Arithmetica},
keywords = {irregularities of distribution; discrepancy; diaphony; digital sequence; van der Corput sequence},
language = {eng},
number = {4},
pages = {321-340},
title = {A generalization of NUT digital (0,1)-sequences and best possible lower bounds for star discrepancy},
url = {http://eudml.org/doc/278911},
volume = {158},
year = {2013},
}

TY - JOUR
AU - Henri Faure
AU - Friedrich Pillichshammer
TI - A generalization of NUT digital (0,1)-sequences and best possible lower bounds for star discrepancy
JO - Acta Arithmetica
PY - 2013
VL - 158
IS - 4
SP - 321
EP - 340
AB - 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.
LA - eng
KW - irregularities of distribution; discrepancy; diaphony; digital sequence; van der Corput sequence
UR - http://eudml.org/doc/278911
ER -