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

sbt(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: 2008-04-04. http://mint.sbg.ac.at/desc_CBoundK3.html

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