Net Defined by OOA

Given a (linear) ordered orthogonal array OOA(bm, s, Sb, T , k) with T ≥ k, a (digital) (m−k, m, s)-net in base b can be constructed [1] [2].

Construction

The net N is constructed based on A as

N = {($\displaystyle \sum_{{j=1}}^{{T}}$$\displaystyle {\frac{{\eta_{i,j}(x_{i,j})}}{{b^{j}}}}$)i=1,…, s  :  x ∈ A}

with ηi,j : Sb↔{0,…, b – 1} denoting arbitrary bijections.

See Also

References

[1]Kenneth Mark Lawrence.
A combinatorial characterization of (t, m, s)-nets in base b.
Journal of Combinatorial Designs, 4(4):275–293, 1996.
doi:10.1002/(SICI)1520-6610(1996)4:4<275::AID-JCD5>3.0.CO;2-C
[2]Gary L. Mullen and Wolfgang Ch. Schmid.
An equivalence between (t, m, s)-nets and strongly orthogonal hypercubes.
Journal of Combinatorial Theory, Series A, 76(1):164–174, October 1996.
doi:10.1006/jcta.1996.0098

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

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