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
Corresponding result for orthogonal arrays and linear codes and OOAs
Corresponding result for sequences
Construction 2 in [2]
Propagation Rule 2 in [3]
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: 2015-09-03.
http://mint.sbg.ac.at/desc_NSRed.html