Publication Details

This article was originally published as SahaRay, R, Adhikari, A and Seberry, J, Critical sets in orthogonal arrays with 7 and 9 levels, Australasian Journal of Combinatorics, 33, 2005, 109-123.


To date very few results are known on the critical sets for a set of Mutually Orthogonal Latin Squares(MOLS). In this paper, we consider Orthogonal Array OA(n2, k + 2, n, 2) constructed from k mutually orthogonal cyclic latin squares of order n and obtain bounds on the possible sizes of the minimal critical sets. In particular, for n = 7 we exhibit a critical set, thereby improving the bound reported in Keedwell (1997). The problem is also addressed for n = 9 and a critical set is also presented.