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''. In this paper, 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：正交阵列在众多应用中扮演着基础性角色。然而，为特定应用构造具有所需参数的正交阵列通常极其困难，有时甚至不可能实现。因此，对正交阵列进行松弛处理以增强灵活性的需求日益增长。后者衍生出名为“近似正交阵列”（nearly-orthogonal arrays）的多种阵列类型，较少见的还有“几乎正交阵列”（almost orthogonal arrays）。本文探讨了三种寻找几乎正交阵列的方法：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的现有结果进行比较，表明它们具有竞争力，并在多种非正交性度量标准下改进了许多现有阵列。我们所有发现的几乎正交阵列均已公开在公共存储库中。