Discarding Parts of the Base for OAs

Given an orthogonal array A with parameters OA(M, s,F_p^u, k), an OA(M, s,F_p^uʹ, k) Aʹ with 1 ≤ uʹ ≤ 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_p^u→F_p^uʹ denote an arbitrary surjective linear mapping. The resulting OA Aʹ is obtained from A as

See Also

• Generalization for arbitrary OOAs

• If uʹ 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 OAs.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2024-09-05. http://mint.sbg.ac.at/desc_CBDiscarding.html