On the lower bound of the discrepancy of (<i>t</i>,<i>s</i>) sequences: I

Mordechay B. Levin

doi:10.1016/j.crma.2016.02.011

Number theory

On the lower bound of the discrepancy of (t,s) sequences: I
[Sur la limite inférieure de la discrépance de (t,s) suites : I]

Présenté par : the Editorial Board

Mordechay B. Levin ¹

¹ Department of Mathematics, Bar-Ilan University, Ramat-Gan, 52900, Israel

Comptes Rendus. Mathématique, Volume 354 (2016) no. 6, pp. 562-565.

Résumé
Abstract

Nous trouvons une limite inférieure pour la discrépance de suites décalées de Niederreiter.

We find the exact lower bound of the discrepancy of shifted Niederreiter's sequences.

Reçu le : 2015-05-25
Accepté le : 2016-02-10
Publié le : 2016-04-11

DOI : 10.1016/j.crma.2016.02.011

Affiliations des auteurs :

Mordechay B. Levin ¹

¹ Department of Mathematics, Bar-Ilan University, Ramat-Gan, 52900, Israel

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     author = {Mordechay B. Levin},
     title = {On the lower bound of the discrepancy of (\protect\emph{t},\protect\emph{s}) sequences: {I}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {562--565},
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     year = {2016},
     doi = {10.1016/j.crma.2016.02.011},
     language = {en},
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Mordechay B. Levin. On the lower bound of the discrepancy of (t,s) sequences: I. Comptes Rendus. Mathématique, Volume 354 (2016) no. 6, pp. 562-565. doi : 10.1016/j.crma.2016.02.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.02.011/

Bibliographie
Cité par

[1] D. Bilyk On Roth's orthogonal function method in discrepancy theory, Unif. Distrib. Theory, Volume 6 (2011) no. 1, pp. 143-184

[2] J. Dick; F. Pillichshammer Digital Nets and Sequences, Discrepancy Theory and Quasi-Monte Carlo Integration, Cambridge University Press, Cambridge, UK, 2010

[3] M. Drmota; R. Tichy Sequences, Discrepancies and Applications, Lecture Notes in Mathematics, vol. 1651, 1997

[4] C. Lemieux Monte Carlo and Quasi-Monte Carlo Sampling, Springer Series in Statistics, Springer, New York, 2009

[5] M.B. Levin On the lower bound of the discrepancy of $(t, s)$ sequences: II http://arXiv.org/abs/1505.04975

[6] H. Niederreiter Random Number Generation and Quasi-Monte Carlo Methods, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 63, SIAM, 1992

[7] S. Tezuka On the discrepancy of generalized Niederreiter sequences, J. Complexity, Volume 29 (2013), pp. 240-247

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