s-Reduction for Sequences

Every (digital) (t, s)-sequence with s > 1 yields a (digital) (t, s−1)-sequence in the same base.

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

This result follows directly from the corresponding results for nets [1, Lemma 2.7 (ii)].

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)

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 for Sequences.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2024-09-05. http://mint.sbg.ac.at/desc_SSRed.html