## Appending *k*th Column

Given a (linear) ordered orthogonal array OOA(*M*, *s*, *S*_{b}, *k*−1, *k*) with *k* ≥ 2, a (linear) OOA(*M*, *s*, *S*_{b}, *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

*x*

_{i,1},…,

*x*

_{i,k−1},

*x*

_{σ(i), 1})

_{i=1,…, s}:

*∈ A}.*

**x**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 *k*th Column.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2008-04-04.
http://mint.sbg.ac.at/desc_ODepthEqualsStrength.html