Extracting Embedded OOA
Given a (digital) (m−k, 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
with ηi,j : Sb↔{0,…, b – 1} denoting arbitrary bijections.
See Also
Special case for orthogonal arrays and codes
For T ≥ k this process can be reversed by net defined by OOA
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: 2024-09-05.
http://mint.sbg.ac.at/desc_OFromN.html