We computationally completely enumerate a number of types of row-column designs up to isotopism, including double, sesqui and triple arrays as known from the literature, and two newly introduced types that we call mono arrays and AO-arrays. We calculate autotopism group sizes for the designs we generate. For larger parameter values, where complete enumeration is not feasible, we generate examples of some of the designs, and generate exhaustive lists of admissible parameters. For some admissible parameter sets, we prove non-existence results. We also give some explicit constructions of sesqui arrays, mono arrays and AO-arrays, and investigate connections to Youden rectangles and binary pseud Youden designs.

翻译：我们通过计算完全枚举了多种类型的行-列设计，直至同构关系，包括文献中已知的双阵列、倍半阵列和三重阵列，以及我们新引入的两种类型——单阵列和AO阵列。我们计算了所生成设计的自同构群大小。对于较大的参数值，在无法进行完全枚举的情况下，我们生成了部分设计的示例，并详尽列出了所有可容许的参数集。针对某些可容许的参数集，我们证明了不存在性结果。我们还给出了倍半阵列、单阵列和AO阵列的一些显式构造，并探讨了它们与Youden矩形和二元伪Youden设计之间的联系。