Group strong orthogonal arrays and their construction methodsGroup strong orthogonal arrays and their construction methodsP. Li et al.

In practical applications, group structures may exist between response variables and input factors in certain computer experiments. The interactions of interest occur exclusively within factors within several disjoint groups. In such experiments, an ideal design ensures superior space-filling properties for each group compared to the overall design, which itself exhibits commendable space-filling characteristics. Inspired by this idea, we introduce the concept of group strong orthogonal arrays, which can be partitioned into distinct groups. Both the overall design and each individual group constitute strong orthogonal arrays, with the strength of each group exceeding that of the entire design. Addressing different strengths and levels, we present the construction methods for three distinct types of such designs, among which two types are column-orthogonal. Orthogonal arrays, difference matrices, and rotation matrices play pivotal roles in the construction process.