Universally Optimal Designs for the Two-dimensional Interference Model

There have been some major advances in the theory of optimal designs for interference models. However, the majority of them focus on one-dimensional layout of the block and the study for two-dimensional interference model is quite limited partly due to technical difficulties. This paper tries to fill this gap. Specifically, it systematically characterizes all possible universally optimal designs simultaneously. Computational issues are also addressed with theoretical backup.