Bound for OAs with Index Unity

For every orthogonal array OA(bk, s, Sb, k), i.e. an orthogonal array with index unity, with k ≥ 2 and b a prime power we have

s\begin{displaymath}\begin{cases}k+1 & \textrm{for $b\leq k$}\\ b+k−2 & \textr… …q k<b$ and $b$ even}\\ b+k−1 & \textrm{otherwise}\end{cases}\end{displaymath}.

Line 1, 2 and 4 are due to [1], and it is shown in [2] that line 1 follows also from the dual Plotkin bound for OAs.

Line 3 as well as the non-existence of an OA(b4, 7, 5, 4) is due to [3].

References

[1]Kenneth A. Bush.
Orthogonal arrays of index unity.
Annals of Mathematical Statistics, 13:426–434, 1952.
MR0049146 (14,125b)
[2]Jürgen Bierbrauer.
Bounds on orthogonal arrays and resilient functions.
Journal of Combinatorial Designs, 3(3):179–183, 1995.
doi:10.1002/jcd.3180030304 MR1324473 (96d:05023)
[3]S. Kounias and C. I. Petros.
Orthogonal arrays of strength three and four with index unity.
Sankhyā, B 37:228–240, 1975.

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. “Bound for OAs with Index Unity.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_CBoundT0.html

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