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 s ≤ b and b a prime power are (generalized) Faure sequences, Niederreiter sequences, and Niederreiter-Xing sequences based on the rational function field.
See Also
Corresponding results for nets, OOAs, and orthogonal arrays and linear codes
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: 2015-09-03.
http://mint.sbg.ac.at/desc_SBoundTrivialT.html