Improved formulation of Audze-Eglājs criterion for space-filling designs

The Audze–Eglājs (AE) criterion was developed to achieve uniform distribution of experimental points in a hypercube. However, the paper shows that the AE criterion provides strongly nonuniform designs due to the effect of boundaries of the hypercube. We propose a simple remedy that lies in the assumption of periodic boundary conditions. The biased behavior of the original AE criterion and excellent performance of the modified criterion is demonstrated using simple numerical examples focused on (i) uniformity of the samples density over the design space and, (ii) statistical sampling efficiency measured through the ability to correctly estimate statistics of functions of random variables.