Logical Equivalence (for Nets with Unbounded m)

Let t, s, and b be fixed. Then the following statements are equivalent. For purely technical reasons they have to be included separately in MINT:

• There is no (digital) (t, m, s)-net in base b with arbitrarily large m.

• For some (large) m, there is no (digital) (t, m, s)-net in base b.

• For some (large) k, there is no (digital) (t, t + k, s)-net in base b.

• If a (tʹ, m, s)-net in base b exists for arbitrary m, then tʹ > t.

• If a (tʹ, tʹ + k, s)-net in base b exists for arbitrary k, then tʹ > t.

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. “Logical Equivalence (for Nets with Unbounded m).” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2024-09-05. http://mint.sbg.ac.at/desc_SBoundLogicalEquivalence.html