Strong orthogonal arrays (SOAs) have received more and more attention recently since they enjoy more desirable space-filling properties than ordinary orthogonal arrays. Among them, the SOAs of strength \(2+\) are the most advisable as they satisfy the same two-dimensional space-filling property as SOAs of strength 3 while having more columns for given run sizes. In addition, column-orthogonality is also a desirable property for designs of computer experiments. Existing column-orthogonal SOAs of strength \(2+\) have limited columns. In this paper, we propose a new class of space-filling designs, called group SOAs of strength \(2+\), and provide construction methods for such designs. The proposed designs can accommodate more columns than column-orthogonal SOAs of strength \(2+\) for given run sizes while satisfying similar stratifications and retaining a high proportion of column-orthogonal columns. Orthogonal arrays and difference schemes play important roles in the construction. The construction procedures are easy to implement and a large amount of group SOAs with \(s^2\) levels are constructed where \(s \ge 2\) is a prime power. In addition, the run sizes of the constructed designs are s times the ones of the orthogonal arrays used in the construction procedure. Thus they are relatively flexible.

强正交阵列（SOA）最近受到越来越多的关注，因为它们比普通正交阵列具有更理想的空间填充特性。其中，强度为\(2+\)的 SOA是最可取的，因为它们满足与强度为 3 的 SOA 相同的二维空间填充特性，同时对于给定的运行大小具有更多的列。此外，列正交性也是计算机实验设计的理想属性。现有强度为\(2+\) 的列正交 SOA具有有限的列。在本文中，我们提出了一类新的空间填充设计，称为强度\(2+\)，并为此类设计提供构造方法。对于给定的运行大小，建议的设计可以容纳比强度为\(2+\) 的列正交 SOA 更多的列，同时满足类似的分层并保留高比例的列正交列。正交阵列和差分方案在构造中起着重要作用。构建过程易于实现，并且构建了大量具有\(s^2\)级别的组 SOA，其中\(s \ge 2\)是素数。此外，构造设计的游程大小是构造过程中使用的正交数组的s倍。因此它们相对灵活。