Niederreiter–Xing Sequence Construction II/III
In [1] and [2] Niederreiter and Xing develop two methods (Niederreiter-Xing (NX) sequence construction II and III) for creating a digital (t, s)-sequence over Fb based on an algebraic function field with full constant field Fb, genus t, and containing at least s + 1 rational places. NX sequence construction III is constructive, assuming that defining equations for the function field are given and that s + 1 rational places are known.
See Also
Construction 18 in [3].
References
| [1] | Harald Niederreiter and Chaoping Xing. Low-discrepancy sequences and global function fields with many rational places. Finite Fields and Their Applications, 2(3):241–273, July 1996. doi:10.1006/ffta.1996.0016 MR1398076 (97h:11080) |
| [2] | 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) |
| [3] | 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 II/III.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2024-09-05.
http://mint.sbg.ac.at/desc_SNX.html