Net Duplication

Every (digital) (t, m, s)-net in base b yields a (digital) (t + 1, m + 1, s)-net in base b [1] [2, Lemma 10]. For digital nets this can be achieved by adding an arbitrary row and column to each generator matrix. In the general case it can be done by replicating the point set b times.

See Also

• Generalization for arbitrary OOAs

• Corresponding result for orthogonal arrays and codes

• Construction 16 in [1]

• Propagation Rule 3 in [3]

References

[1]	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.
[2]	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)
[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. “Net Duplication.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2024-09-05. http://mint.sbg.ac.at/desc_NDuplication.html