Constructions of optimal 2-level orthogonal arrays with repeated rows

. In this paper, the definition of the 2-tuples distribution matrix is proposed, and some properties of 2-tuples distribution matrix are demonstrated. Based on these results, we introduce a new method to construct optimal orthogonal arrays OA lambda(k, 2) having a row that is repeated m = a over bar times. A class of optimal orthogonal arrays OA lambda(k, 2) having a row that is repeated m = a over bar times are constructed with the help of the 2-tuples distribution matrix of the orbit Ok(x), where lambda = 1 +2 + center dot center dot center dot + a over bar , a over bar = k-12 and k is an odd prime.