On the existence of orthogonal arrays OA(3,5,4n+2)

By an OA(3,5,v) we mean an orthogonal array (OA) of order v, strength t=3, index unity and 5 constraints. The existence of such an OA implies the existence of a pair of mutually orthogonal Latin squares (MOLSs) of side v. After Bose, Shrikhande and Parker (1960) [2] disproved the long-standing Euler conjecture in 1960, one has good reason to believe that an OA(3,5,4n+2) exists for any integer n⩾2. So far, however, no construction of an OA(3,5,4n+2) for any value of n has been given. This paper tries to fill this gap in the literature by presenting an OA(3,5,4n+2) for infinitely many values of n⩾62.