Niederreiter–Xing Sequence Construction III Using Non-Rational Places

In [1] Niederreiter and Xing develop a method (Niederreiter-Xing (NX) sequence construction III) for creating a digital (t, s)-sequence over Fb based on an algebraic function field of genus g containing s + 1 distinct places P, P1,…, Ps with deg P = 1. The t-parameter is bounded by

tg + $\displaystyle \sum_{{i=1}}^{{s}}$(deg Pi − 1).

NX sequence III is constructive, assuming that defining equations for the function field are given and that appropriate places P, P1,…, Ps are known.

Usually, the best results are achieved if only rational places are used. However, a number of function fields are known where better results can be obtained by including a small number of places of higher degree.

See Also

References

[1]Chaoping Xing and Harald Niederreiter.
A construction of low-discrepancy sequences using global function fields.
Acta Arithmetica, 73(1):87–102, 1995.
MR1358190 (96g:11096)
[2]Andrew T. Clayman, Kenneth Mark Lawrence, Gary L. Mullen, Harald Niederreiter, and Neil J. A. Sloane.
Updated tables of parameters of (t, m, s)-nets.
Journal of Combinatorial Designs, 7(5):381–393, 1999.
doi:10.1002/(SICI)1520-6610(1999)7:5<381::AID-JCD7>3.0.CO;2-S MR1702298 (2000d:05014)

Copyright

Copyright © 2004, 2005, 2006, 2007, 2008, 2009, 2010 by Rudolf Schürer and Wolfgang Ch. Schmid.
Cite this as: Rudolf Schürer and Wolfgang Ch. Schmid. “Niederreiter–Xing Sequence Construction III Using Non-Rational Places.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_SNX3NonRationalPlaces.html

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