## Base Expansion for OOAs

Given an ordered orthogonal array A with parameters OOA(*b*^{um}, *s*,**F**_{b}, *uT *, *uk*) for *u* ≥ 1, an OOA((*b*^{u})^{m}, *s*,**F**_{bu}, *T *, *k*) can be obtained. If A is linear, the resulting OOA Aʹ is linear over **F**_{b}, but in general not over **F**_{bu}. Thus Aʹ is not linear.

### Construction

Let *a*_{1},…, *a*_{u} ∈ **F**_{bu} denote a basis of **F**_{bu} over **F**_{b} and let *φ* : **F**_{b}^{u}↔**F**_{bu} be defined as *φ*(*x*_{1},…, *x*_{u}) := *a*_{1}*x*_{1} + … + *a*_{u}*x*_{u}. Then Aʹ is constructed based on A as

*φ*(

*x*

_{i,1},…,

*x*

_{i,u}),…,

*φ*(

*x*

_{i,u(T−1)+1},…,

*x*

_{i,uT}))

_{i=1,…, s}:

*∈ A}.*

**x**### See Also

For

*T*→∞ the corresponding result for nets is obtained

### 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. “Base Expansion for OOAs.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2015-09-03.
http://mint.sbg.ac.at/desc_OBExp.html