Bound for OAs with Strength k = 2

An orthogonal array OA(M, s, Sb, 2) can exist only if

s$\displaystyle {\frac{{M−1}}{{b−1}}}$.

This result follows trivially from the Rao bound [1].

For linear OAs, the same result can be established directly by considering the generator matrix: Since any two columns must be linearly independent, s cannot be larger than the size of the largest set of pairwise linearly independent vectors in Fbm.


[1]Calyampudi Radhakrishna Rao.
Factorial experiments derivable from combinatorial arrangements of arrays.
Supplement to the Journal of the Royal Statistical Society, 9:128–139, 1947.


Copyright © 2004, 2005, 2006, 2007, 2008, 2009, 2010 by Rudolf Schürer and Wolfgang Ch. Schmid.
Cite this as: Rudolf Schürer and Wolfgang Ch. Schmid. “Bound for OAs with Strength k = 2.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04.

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