Orthogonal arrays play a fundamental role in many applications. However, constructing orthogonal arrays with the required parameters for an application usually is extremely difficult and, sometimes, even impossible. Hence there is an increasing need for a relaxation of orthogonal arrays to allow a wider flexibility. The latter has lead to various types of arrays under the name of ``nearly-orthogonal arrays'', and less often ``almost orthogonal arrays''. The aim of this paper is twofold. On the one hand, we review all the existing relaxations, comparing and discussing them in depth. On the other hand, we explore how to find almost orthogonal arrays three ways: using integer programming, local search meta-heuristics and algebraic methods. We compare all our search results with the ones existing in the literature, and we show that they are competitive, improving some of the existing arrays for many non-orthogonality measures. All our found almost orthogonal arrays are available at a public repository.

翻译：正交阵列在许多应用中发挥着基础性作用。然而，针对特定应用需求构造具有所需参数的正交阵列通常极为困难，有时甚至不可能实现。因此，对正交阵列进行松弛以提供更大灵活性的需求日益增长。这催生了多种以“近似正交阵列”为名，较少情况下称为“几乎正交阵列”的阵列类型。本文的目标是双重的。一方面，我们系统回顾了所有现有的松弛形式，对其进行了深入的比较与讨论。另一方面，我们探索了三种寻找几乎正交阵列的方法：使用整数规划、局部搜索元启发式算法以及代数方法。我们将所有搜索结果与文献中已有的结果进行比较，结果表明这些方法具有竞争力，并在多种非正交性度量指标上改进了部分现有阵列。我们找到的所有几乎正交阵列均存放于公共存储库中可供获取。