In this paper, in view of the Rao’s inequalities on the parameters of an orthogonal array, we define some extended matrices for asymmetric orthogonal arrays of strength $t$ $(t\ge 2)$. According to these matrices, necessary conditions for the existence of tight asymmetric orthogonal arrays of strengths 2 and 4 described by Mukerjee and Wu (1995) are generalized to the existence of tight asymmetric orthogonal arrays of strength $t$, and examples of the nonexistence of tight asymmetric orthogonal arrays with high strength are interpreted. Furthermore, some conditions on the additional $p$ runs are determined, which guarantee that the orthogonal array plus $p$ run design is $D$-optimal.

在本文中，鉴于正交阵列参数上的Rao不等式，我们定义了一些非对称强度正交阵列的扩展矩阵 $吨$ $(吨\ge 2)$. 根据这些矩阵，将 Mukerjee 和 Wu (1995) 描述的强度 2 和 4 的紧非对称正交阵列存在的必要条件推广到强度的紧非对称正交阵列的存在$吨$，并且解释了不存在具有高强度的紧密非对称正交阵列的例子。此外，一些附加条件$磷$ 确定运行，这保证正交阵列加上 $磷$ 运行设计是 $D$-最佳。