t-Expansion

It follows directly from the definition of (t, m, s)-nets that every (digital) (t, m, s)-net is also a (digital) (tʹ, m, s)-net in the same base for all tʹ = t,…, m. [1, Lemma 2.6 (i)]

See Also

• Construction 1 in [2]

• Corresponding result for orthogonal arrays and codes and OOAs

• Corresponding result for sequences

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.

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