Orthogonal array is one of the important research subjects in combinatorial design theory and experimental design theory, and it is widely applied to statistics, computer science, coding theory and cryptography. There are many constructions and results for orthogonal array of strength 2, however the results on orthogonal array of strength \(t\ge 3\) are rare. In this paper, we first present two new effective constructions for orthogonal arrays of strength \(t\ge 3\) based on large sets of orthogonal arrays. Second, many infinite families of large sets of orthogonal arrays are obtained and then some new series of orthogonal array of strength \(t\ge 3\) are produced.

正交阵是组合设计理论和实验设计理论中的重要研究课题之一，广泛应用于统计学、计算机科学、编码理论和密码学等领域。强度为2的正交阵的构造和结果很多，而强度为\(t\ge 3\)的正交阵的结果很少。在本文中，我们首先提出了两种新的有效结构，用于基于大型正交阵列集的强度\(t\ge 3\)的正交阵列。其次，得到许多正交阵列大集的无限族，然后产生一些新的强度\(t\ge 3\)的正交阵列系列。