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

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.