Construction for Strength k = 1

For all b, m ≥ 1, and s, the multiset consisting of the points (n/b,…, n/b) ∈ [0, 1)s for n = 0,…, b−1 each with multiplicity bm−1 is a (m−1, m, s) = (t, t + 1, s)-net in base b.

A digital net over Fb can be obtained by using any set of s m×m-matrices over Fb, given that non of the first row vectors of the generator matrices is the zero vector.

See Also

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.

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. “Construction for Strength k = 1.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_NK1.html

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