## Trivial Lower Bound on *t*

For any (*t*, *m*, *s*)-net in base *b*, *t* is always greater or equal to 0.

This follows immediately from the definition of (*t*, *m*, *s*)-nets.

### Nets Meeting this Bound

(*t*, *m*, *s*)-nets meeting this bound are (0, *m*, *s*)-nets. They have either *m* = 0 (e.g. trivial nets), *m* = 1 (e.g. nets with strength *k* = 1, or *s* ≤ *b* + 1 (e.g., nets derived from (0, *s*)-sequences).

Nets in base *b* with *m* > 1 and *s* > *b* + 1 must have *t* ≥ 1 and therefore cannot meet this bound because of *s*-reduction, *m*-reduction, and the non-existence of a (0, 2, *b* + 2)-net due to the mutually orthogonal hypercube bound.

### See Also

Generalization for arbitrary OOAs

Corresponding results for orthogonal arrays and linear codes and sequences

### 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 Lower Bound on *t*.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2008-04-04.
http://mint.sbg.ac.at/desc_NBoundTrivialT.html