s-Reduction

Every (digital) (t, m, s)-net with s > 1 yields a (digital) (t, m, s−1)-net in the same base [1, Lemma 2.7 (i)].

The new net is obtained by projecting the point set into any of the (s−1)-dimensional faces of the unit cube. If the net is digital, the new digital net is obtained by discarding one generator matrix.

See Also

References

[1]Harald Niederreiter.
Point sets and sequences with small discrepancy.
Monatshefte für Mathematik, 104(4):273–337, December 1987.
doi:10.1007/BF01294651 MR918037 (89c:11120)
[2]Gary L. Mullen, Arijit Mahalanabis, and Harald Niederreiter.
Tables of (t, m, s)-net and (t, s)-sequence parameters.
In Harald Niederreiter and Peter Jau-Shyong Shiue, editors, Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, volume 106 of Lecture Notes in Statistics, pages 58–86. Springer-Verlag, 1995.
[3]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. “s-Reduction.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_NSRed.html