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

Experimental designs that spread points apart from each other on projections are important for computer experiments, when not necessarily all factors have a substantial influence on the response. We provide a theoretical framework for generating designs that have quasi-optimal separation distance on all 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 the class of densest packing-based maximum projection designs, which outperform existing types of space-filling designs in many scenarios.