  The main interest of this paper is to study the relationship between the
low-discrepancy sequence and the static solution to the multi-bodies problem in
high-dimensional space. An assumption that the static solution to the
multi-bodies problem is a low-discrepancy sequence is proposed. Considering the
static solution to the multi-bodies problem corresponds to the minimum
potential energy principle, we further assume that the distribution of the
bodies is the most uniform when the potential energy is the smallest. To verify
the proposed assumptions, a dynamical evolutionary model (DEM) based on the
minimum potential energy is established to find out the static solution. The
central difference algorithm is adopted to solve the DEM and an evolutionary
iterative scheme is developed. The selection of the mass and the damping
coefficient to ensure the convergence of the evolutionary iteration is
discussed in detail. Based on the DEM, the relationship between the potential
energy and the discrepancy during the evolutionary iteration process is
studied. It is found that there is a significant positive correlation between
them, which confirms the proposed assumptions. We also combine the DEM with the
restarting technique to generate a series of low-discrepancy sequences. These
sequences are unbiased and perform better than other low-discrepancy sequences
in terms of the discrepancy, the potential energy, integrating eight test
functions and computing the statistical moments for two practical stochastic
problems. Numerical examples also show that the DEM can not only generate
uniformly distributed sequences in cubes, but also in non-cubes.
