Existence of super-simple OA_{\lambda }(3, 5, v)^{\prime }s

It was proved recently that a super-simple orthogonal array (SSOA) of strength \(t\) and index \(\lambda \ge 2\) is equivalent to a minimum detecting array (DTA). In computer software tests in component-based systems, such a DTA can be used to generate test suites that are capable of locating \(d=\lambda -1\) \(t\) -way interaction faults and detect whether there are more than \(d\) interaction faults. It is proved in this paper that an SSOA of strength \(t=3\) , index \(\lambda \ge 2\) and degree \(k=5\) , or an SSOA \(_{\lambda }(3,5,v)\) , exists if and only if \(\lambda \le v\) excepting possibly a handful of cases.