This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Bierbrauer. A direct approach to linear programming bounds for codes and tms-nets. Des. Codes Cryptogr., 42:127–143, 2007.
A. GarcÃa and H. Stichtenoth. A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound. Invent. Math., 121:211–222, 1995.
K. M. Lawrence. Combinatorial Bounds and Constructions in the Theory of Uniform Point Distributions in Unit Cubes, Connections with Orthogonal Arrays and a Poset Generalization of a Related Problem in Coding Theory. PhD thesis, University of Wisconsin, Madison, 1995.
K. M. Lawrence. A combinatorial characterization of (t, m, s)-nets in base b. J. Combin. Des., 4:275–293, 1996.
G. Larcher and W. Ch. Schmid. Multivariate Walsh series, digital nets and quasi-Monte Carlo integration. In H. Niederreiter and P. J.-S. Shiue, editors, Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, volume 106 of Lecture Notes in Statistics, pages 252–262. Springer-Verlag, Berlin, 1995.
G. L. Mullen and W. Ch. Schmid. An equivalence between (t, m, s)-nets and strongly orthogonal hypercubes. J. Combin. Theory Ser. A, 76:164–174, 1996.
W. J. Martin and D. R. Stinson. Association schemes for ordered orthogonal arrays and (t, m, s)-nets. Canad. J. Math., 51:326–346, 1999.
W. J. Martin and D. R. Stinson. A generalized Rao bound for ordered orthogonal arrays and (t, m, s)-nets. Canad. Math. Bull., 42:359–370, 1999.
W. J. Martin and T. I. Visentin. A dual Plotkin bound for (T, M, S)-nets. IEEE Trans. Inform. Theory, 53:411–415, 2007.
H. Niederreiter. Point sets and sequences with small discrepancy. Monatsh. Math., 104:273–337, 1987.
H. Niederreiter. Random Number Generation and Quasi-Monte Carlo Methods. SIAM, Philadelphia, 1992.
H. Niederreiter and G. Pirsic. Duality for digital nets and its applications. Acta Arith., 97:173–182, 2001.
H. Niederreiter and C. P. Xing. Low-discrepancy sequences and global function fields with many rational places. Finite Fields Appl., 2:241–273, 1996.
H. Niederreiter and C. P. Xing. Quasirandom points and global function fields. In S. Cohen and H. Niederreiter, editors, Finite Fields and Applications, volume 233 of London Math. Soc. Lecture Note Ser., pages 269–296. Cambridge University Press, Cambridge, 1996.
H. Niederreiter and C. P. Xing. Nets, (t, s)-sequences, and algebraic geometry. In P. Hellekalek and G. Larcher, editors, Random and Quasi-Random Point Sets, volume 138 of Lecture Notes in Statistics, pages 267–302. Springer-Verlag, Berlin, 1998.
M. Y. Rosenbloom and M. A. Tsfasman. Codes for the m-metric. Probl. Inf. Transm., 33:55–63, 1997.
W. Ch. Schmid. Shift-nets: a new class of binary digital (t, m, s)-nets. In H. Niederreiter , editors, Monte Carlo and Quasi-Monte Carlo Methods 1996, volume 127 of Lecture Notes in Statistics, pages 369–381. Springer-Verlag, Berlin, 1998.
W. Ch. Schmid and R. Wolf. Bounds for digital nets and sequences. Acta Arith., 78:377–399, 1997.
C. P. Xing and H. Niederreiter. A construction of low-discrepancy sequences using global function fields. Acta Arith., 73:87–102, 1995.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schürer, R. (2008). A New Lower Bound on the t-Parameter of (t, s)-Sequences. In: Keller, A., Heinrich, S., Niederreiter, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74496-2_37
Download citation
DOI: https://doi.org/10.1007/978-3-540-74496-2_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74495-5
Online ISBN: 978-3-540-74496-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)