Bounds on orthogonal arrays and resilient functions

摘要

AbstractThe only known general bounds on the parameters oforthogonal arraysare those given by Rao in 1947 J. Roy. Statist. Soc. 9 (1947), 128–139 for generalOAγ(t,k,v) and by Bush Ann. Math. Stat. 23, (1952), 426–434 3in 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 caset ⩾ v, and more importantly a new explicit bound which for large values oft(thestrengthof 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. © 1995 John Wiley