Trivial Upper Bound on s

Requiring s ≤ ∞ is a trivial upper bound on the dimension s of a (t, m, s)-net because it allows arbitrarily large values for s.

Nets Meeting this Bound

Nets with arbitrarily large s exist. In particular, nets with m = t (arbitrary net) and m = t + 1 can have arbitrarily large s.

See Also

• Generalization for arbitrary OOAs

• Corresponding result for orthogonal arrays

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