Trivial Lower Bound on t for Sequences

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

This follows immediately from the definition of (t, s)-sequences and the non-existence of (t, m, s)-nets with t < 0.

Sequences Meeting this Bound

(t, s)-sequences in base b meeting this bound are (0, s)-sequences. They cannot have b > s because of s-reduction for sequences, net from sequence, and the non-existence of a (0, 2, b + 2)-net due to the mutually orthogonal hypercube bound.

Prominent examples of digital (0, s)-sequences with sb and b a prime power are (generalized) Faure sequences, Niederreiter sequences, and Niederreiter-Xing sequences based on the rational function field.

See Also

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 for Sequences.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_SBoundTrivialT.html

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