A Bound by Schmid and Wolf
Schmid and Wolf show that neither a digital (2, 8, 7)-net [1, Lemma 4] nor a digital (2, 7, 8)-net [1, Proposition 2] over ℤ2 can exist. An analysis of the proof shows that a linear ordered orthogonal array OOA(28, 7, ℤ2, 3, 6) and a linear OOA(27, 8, ℤ2, 2, 5) cannot exist either.
The second result follows also from the linear programming bound.
References
| [1] | Wolfgang Ch. Schmid and Reinhard Wolf. Bounds for digital nets and sequences. Acta Arithmetica, 78(4):377–399, 1997. |
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. “A Bound by Schmid and Wolf.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2015-09-03.
http://mint.sbg.ac.at/desc_OBoundSchmidWolf.html