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


[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 © 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: 2008-04-04.

Show usage of this method