Trivial Upper Bound on the Number of Factors for OOAs

Requiring s ≤ ∞ is a trivial upper bound on the number of factors s of an ordered orthogonal array OOA(M, s, S_b, T , k) because it allows arbitrarily large values of s.

OOAs Meeting this Bound

OOAs with arbitrarily large s exist. In particular, OOAs with k = 0 (arbitrary OOA) and k = 1 (embedding of line OA / dual of parity check code) can have arbitrarily large s for any fixed M.

See Also

• For T = 1 the special case for orthogonal arrays is obtained.

• For T →∞ the special case 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. “Trivial Upper Bound on the Number of Factors for OOAs.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. http://mint.sbg.ac.at/desc_OBoundTrivialS.html