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_b^u, T , k) can be obtained. If A is linear, the resulting OOA Aʹ is linear over F_b, but in general not over F_b^u. Thus Aʹ is not linear.

Construction

Let a₁,…, a_u ∈ F_b^u denote a basis of F_b^u over F_b and let φ : F_b^u↔F_b^u be defined as φ(x₁,…, x_u) := a₁x₁ + … + a_ux_u. Then Aʹ is constructed based on A as

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: 2024-09-05. http://mint.sbg.ac.at/desc_OBExp.html