Extracting Embedded OOA

Given a (digital) (mk, m, s)-net N in base b, a (linear) ordered orthogonal array A with parameters OOA(bm, s, Sb, T , k) can be constructed for all T with T k/s [1] [2]. If N is digital over Fb, A is linear and its dual is a linear [(s, T ), sT m, k + 1]-NRT-code over Fb.

Construction

A is formed based on the T leading digits in the b-adic expansion of the coordinates of the points of N. More formally, A is obtained from N as

A = {(ηi,j−1(⌊bjxi⌋ modb))(i, j) ∈ {1,…, s}×{1,…, T}  :  xN}

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. “Extracting Embedded OOA.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_OFromN.html

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