Base Expansion for OOAs

Given an ordered orthogonal array A with parameters OOA(bum, s,Fb, uT , uk) for u ≥ 1, an OOA((bu)m, s,Fbu, T , k) can be obtained. If A is linear, the resulting OOA Aʹ is linear over Fb, but in general not over Fbu. Thus Aʹ is not linear.

Construction

Let a1,…, auFbu denote a basis of Fbu over Fb and let φ : FbuFbu be defined as φ(x1,…, xu) := a1x1 + … + auxu. Then Aʹ is constructed based on A as

Aʹ = {(φ(xi,1,…, xi,u),…, φ(xi,u(T−1)+1,…, xi,uT))i=1,…, s  :  xA}.

See Also

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: 2008-04-04. http://mint.sbg.ac.at/desc_OBExp.html

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