Base Reduction
Every (digital) (t, m, s)-net in base bu with u ≥ 1 is a (digital) (tʹ, um, s)-net in base b with
tʹ = min{ut + (u – 1)(s – 1), um}.
For general nets the result is due to [1, Lemma 9], for digital nets it is due to [2].
See Also
Base reduction for affine caps
Construction 26 in [3].
Propagation Rule 6 in [4]
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] | Harald Niederreiter and Chaoping Xing. Constructions of digital nets. Acta Arithmetica, 102(2):189–197, 2002. MR1889629 (2003a:11092) |
| [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) |
| [4] | Harald Niederreiter. Constructions of (t, m, s)-nets and (t, s)-sequences. Finite Fields and Their Applications, 11(3):578–600, August 2005. doi:10.1016/j.ffa.2005.01.001 MR2158777 (2006c:11090) |
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. “Base Reduction.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2024-09-05.
http://mint.sbg.ac.at/desc_NBRed.html