SahaRay, Rita; Adhikari, Avishek; and Seberry, Jennifer R., 2005, Critical sets in orthogonal arrays with 7 and 9 levels, Australasian Journal of Combinatorics, 33, 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 particulat, 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.