The generalized and modified Halton sequences in Cantor bases

Dušan Bednařík , Poj Lertchoosakul , Diego Marques , Pavel Trojovský


This paper aims to generalize results that have appeared in Atanassov (Math Balk New Ser 18(1–2):15–32, 2004). We consider here variants of the Halton sequences in a generalized numeration system, called the Cantor expansion, with respect to arbitrary sequences of permutations of the Cantor base. We first show that they provide a wealth of low-discrepancy sequences by giving an estimate of (star) discrepancy bound of the generalized Halton sequence in bounded Cantor bases. Then we impose certain conditions on the sequences of permutations of the Cantor base which are analogous, but not straightforward, to the modified Halton sequence introduced by E.I. Atanassov. We show that this modified Halton sequence in Cantor bases attains a better estimate of the (star) discrepancy bound than the generalized Halton sequence in Cantor bases.
Author Dušan Bednařík
Dušan Bednařík,,
, Poj Lertchoosakul (FMPI / IM)
Poj Lertchoosakul,,
- Institute of Mathematics
, Diego Marques
Diego Marques,,
, Pavel Trojovský
Pavel Trojovský,,
Journal seriesMonatshefte Fur Mathematik, ISSN 0026-9255, (A 25 pkt)
Issue year2019
Publication size in sheets1.4
Keywords in EnglishHalton sequence, van der Corput sequence, Hammersley point set, low-discrepancy sequence, pseudorandom number, Cantor expansion
Languageen angielski
LicenseOther; published final; Uznanie Autorstwa (CC-BY); with publication
Score (nominal)25
ScoreMinisterial score = 25.0, 22-01-2019, ArticleFromJournal
Ministerial score (2013-2016) = 25.0, 22-01-2019, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 0.716 (2) - 2016=0.632 (5)
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