A methodology is proposed for construction of uniformly distributed point sets within a design domain using an analogy to a dynamical system of interacting particles. It is shown that the distance-based ϕ_p criterion of optimality can be viewed as a potential energy of a system of charged particles. The potential energy is employed in derivation of the equations of motion of the particles. The dissipative dynamical system of mutually repelling particles can be simulated to achieve optimal and near-optimal arrangements of points (the design). The design domain is selected to be an N_var-dimensional unit hypercube, with N_var being the number of variables (factors). The number of points is equal to the number of simulations (levels). The ϕ_p criterion guarantees that the points are spread uniformly within the design domain. Periodicity assumption of the design domain is shown to be an elegant solution how to obtain statistically uniform coverage of the design domain. Solution to such an N-body system is presented. The designs obtained are shown to outperform the existing designs being optimized for multidimensional numerical integration.

Keywords: ϕ_p criterion, Maximin criterion, Audze-Eglajs Uniform design, Low-discrepancy, Space-filling design, Design of Experiments, Monte Carlo Integration, Periodic space.