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

Abstract

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.