  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.
