Critical sets in orthogonal arrays with 7 and 9 levels

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(n, 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.