Lattice-based designs possessing quasi-optimal separation distance on all projections

Abstract: Experimental designs that spread out points apart from each other on projections are important for computer experiments when not necessarily all factors have substantial influence on the response. We provide a theoretical framework to generate designs that possess quasi-optimal separation distance on all of the projections and quasi-optimal fill distance on univariate margins. The key is to use special techniques to rotate certain lattices. One such type of design is densest packing-based maximum projection designs, which outperform existing types of space-filling designs in many scenarios. Computer code to generate these designs is provided in R package LatticeDesign.