## Discarding Parts of the Base for OOAs

Given an ordered orthogonal array A with parameters OOA(*M*, *s*,**F**_{pu}, *T *, *k*), an OOA(*M*, *s*,**F**_{puʹ}, *T *, *k*) Aʹ with 1 ≤ *u*ʹ ≤ *u* can be constructed. If *M* is not a power of *p*^{uʹ}, the resulting OOA listed by MinT is Aʹ duplicated *p*^{v} times with *v* such that the number of runs is equal to the smallest power of *p*^{uʹ} exceeding *M*.

### Construction

Let *φ* : **F**_{pu}→**F**_{puʹ} denote an arbitrary surjective linear mapping. The resulting OOA Aʹ is obtained from A as

*φ*(

*x*

_{i,1}),…,

*φ*(

*x*

_{i,T }))

_{i=1,…, s}:

*∈ A}.*

**x**### See Also

Special case for orthogonal arrays

If

*u*ʹ divides*u*, stronger propagation rules are available, namely {base reduction, XXX} and trace code

### 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. “Discarding Parts of the Base for OOAs.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2008-04-04.
http://mint.sbg.ac.at/desc_OBDiscarding.html