Arbitrary (t, s)-Sequence for Large s

For any given base b and dimension s, there is a t such that a digital (t, s)-sequence over Fb exists.

For instance, the Niederreiter sequence [1] exists over all finite fields Fb and in all dimensions s and has

t$\displaystyle \sum_{{i=1}}^{{s}}$(deg pi − 1),

with pi denoting the ith monic irreducible polynomial over Fb ordered by degree.

References

[1]Harald Niederreiter.
Low-discrepancy and low-dispersion sequences.
Journal of Number Theory, 30(1):51–70, September 1988.
doi:10.1016/0022-314X(88)90025-X MR960233 (89k:11064)

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. “Arbitrary (t, s)-Sequence for Large s.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_STInfSInf.html

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