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

t ≤ g + $\displaystyle \sum_{{i=1}}^{{s}}$(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: 2015-09-03. http://mint.sbg.ac.at/desc_SNX3NonRationalPlaces.html

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