## Depth Reduction

Given a (linear) ordered orthogonal array OOA(*M*, *s*, *S*_{b}, *T *, *k*) with (*T * – 1)*s* ≥ *k*, a (linear) OOA(*M*, *s*, *S*_{b}, *T *−1, *k*) can be constructed.

### The Construction for OOAs

The new OOA Aʹ is obtained by discarding the columns for depth *T * from the original array A, i.e., as

*x*

_{i,1},…,

*x*

_{i,T −1})

_{i=1,…, s}:

*∈ A}.*

**x**If A is linear, a generator matrix of Aʹ is obtained by dropping the columns for depth *T * from the generator matrix of A.

### See Also

Discarding a different set of columns leads to the propagation rule discarding factors

If

*T*≥*k*, this process can be reversed using appending*k*th column for*T*>*k*.

### 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. “Depth Reduction.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2015-09-03.
http://mint.sbg.ac.at/desc_ODepthReduction.html