Geodesic
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]

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Levin, Mordechay B.1
1 Department of Mathematics, Bar-Ilan University, Ramat-Gan, 52900, Israel
Comptes Rendus. Mathématique, Tome 354 (2016) no. 6, pp. 562-565.

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

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

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.02.011

Levin, Mordechay B. 1

1 Department of Mathematics, Bar-Ilan University, Ramat-Gan, 52900, Israel 
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Levin, Mordechay B. On the lower bound of the discrepancy of (t,s) sequences: I. Comptes Rendus. Mathématique, Tome 354 (2016) no. 6, pp. 562-565. doi : 10.1016/j.crma.2016.02.011. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2016.02.011/

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

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

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

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

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

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

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

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