Generalized (u, u+v)-Construction for Nets

The following construction for nets is an immediate consequence of the generalized (u, u + v)-construction for OOAs, see [1, Corollary 3].

Let N1,…, Nr be r digital (ti, mi, si)-nets, all over Fb, with b ≥ r and s1 ≤ ⋯ ≤ sr. Then a digital (t, m, s)-net over Fb with

s = $\displaystyle \sum_{{i=1}}^{{r}}$si,        m = $\displaystyle \sum_{{i=1}}^{{r}}$mi,    and    t ≤ m + 1 – $\displaystyle \min_{{i=1,\ldots,r}}^{}$(r + 1 – i)(mi – ti + 1)

can be constructed.

Special Cases

See Also

References

[1]Rudolf Schürer and Wolfgang Ch. Schmid.
MinT - new features and new results.
In Pierre LʹEcuyer and Art B. Owen, editors, Monte Carlo and Quasi-Monte Carlo Methods 2008, pages 171–189. Springer-Verlag, 2009.
doi:10.1007/978-3-642-04107-5_10

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. “Generalized (u, u+v)-Construction for Nets.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2024-09-05. http://mint.sbg.ac.at/desc_NGeneralizedUUPlusV.html

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