Revised schematic Latin hypercube designs

Association schemes, as a particularly important type of combinatorial structure, find significant applications in various fields. An array is said to be schematic if all of its runs, when classified by a certain row distance, form an association scheme. By relaxing the conditions of association schemes, the definition of revised schematic arrays was proposed. However, due to the complexity of the properties of revised schematic arrays, their corresponding construction methods and existence results are relatively scattered. This paper focuses on a particularly important class of revised schematic arrays, specifically revised schematic Latin hypercube designs, and proposes two efficient and novel construction methods. Finally, some constructed examples are provided to demonstrate the results.