Simplex based space filling designs

Space filling designs are important for deterministic computer experiments. Even a single experiment can be very time consuming and can have many input parameters. Furthermore the underlying function generating the output is often nonlinear. Thus, the computer experiment has to be designed carefully. There exist many design criteria, which can be numerically optimized. Here, a method is developed, which does not need algorithmic optimization. A mesh of nearly regular simplices is constructed and the vertices of the simplices are used as potential design points. The extraction of a design from these meshes is very fast and easy to implement once the underlying mesh has been constructed. The extracted designs are highly competitive regarding the maximin design criterion and it is easy to extract designs for nonstandard design spaces.