Appending kth Column
Given a (linear) ordered orthogonal array OOA(M, s, Sb, k−1, k) with k ≥ 2, a (linear) OOA(M, s, Sb, k, k) can be constructed.
Construction
The new OOA Aʹ is constructed as follows base on A: Let σ denote a permutation of {1,…, s} without fixed points. Then Aʹ is given by
If A is linear, a generator matrix of Aʹ can be obtained in a similar way.
See Also
This process can be reversed by depth reduction, therefore OOAs with depth k and depth k−1 are equivalent.
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. “Appending kth Column.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2024-09-05.
http://mint.sbg.ac.at/desc_ODepthEqualsStrength.html