Large High-Dimensional Nets with Fixed Strength

For a fixed strength k and base b, digital (m−k, m, s)-nets over Fb can be constructed for arbitrarily large values of s, given that m is also allowed to grow.

For any given dimension s we choose m such that

sk ≤ $\displaystyle {\frac{{b^{m}−1}}{{b−1}}}$.

Then the first k rows of the generator matrices C1,…,Cs can be filled using the (bm − 1)/(b−1) linearly independent vectors in Fbm. Therefore s is unbounded if m is unbounded.

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. “Large High-Dimensional Nets with Fixed Strength.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2024-09-05. http://mint.sbg.ac.at/desc_NMInfSInf.html

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