Trivial Upper Bound on the Number of Factors

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

Orthogonal Arrays Meeting this Bound

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

See Also

• Generalization for arbitrary OOAs

• Corresponding result for nets

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