Bounds on orthogonal arrays and resilient functions

Document Type

Article

Publication Date

1995

Department

Department of Mathematical Sciences

Abstract

The only known general bounds on the parameters of orthogonal arrays are those given by Rao in 1947 [J. Roy. Statist. Soc. 9 (1947), 128–139] for general OAγ(t,k,v) and by Bush [Ann. Math. Stat. 23, (1952), 426–434] [3] in 1952 for the special case γ = 1. We present an algebraic method based on characters of homocyclic groups which yields the Rao bounds, the Bush bound in case t ⩾ v, and more importantly a new explicit bound which for large values of t (the strength of the array) is much better than the Rao bound. In the case of binary orthogonal arrays where all rows are distinct this bound was previously proved by Friedman [Proc. 33rd IEEE Symp. on Foundations of Comput. Sci., (1992), 314–319] in a different setting. We also note an application to resilient functions.

Publisher's Statement

© 1995 John Wiley & Sons, Inc. Publisher’s version of record: https://doi.org/10.1002/jcd.3180030304

Publication Title

Journal of Combinatorial Designs

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