Bose–Bush Bound for OAs with Strength 3
Let a = (bt − 1)/(b−1). For every orthogonal array OA(bt+3, s, Sb, 3) with (b – 1)2(b – 2) ≠ 0(mod as+2), we must have
s ≤ bt(b + 1) + a−1.
This bound is due to [1], which contains a number of bounds for OAs with strength 2 and 3. Most of these bounds, however, are only useful for OAs where the index is not a power of b.
This bound is always stronger than the Rao bound.
References
| [1] | Raj Chandra Bose and Kenneth A. Bush. Orthogonal arrays of strength two and three. Annals of Mathematical Statistics, 23:508–524, 1952. MR0051204 (14,442c) |
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. “Bose–Bush Bound for OAs with Strength 3.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2015-09-03.
http://mint.sbg.ac.at/desc_CBoundK3.html