  Distributing points on a (possibly high-dimensional) sphere with minimal
energy is a long-standing problem in and outside the field of mathematics. This
paper considers a novel energy function that arises naturally from statistics
and combinatorial optimization, and studies its theoretical properties. Our
result solves both the exact optimal spherical point configurations in certain
cases and the minimal energy asymptotics under general assumptions. Connections
between our results and the L1-Principle Component Analysis and Quasi-Monte
Carlo methods are also discussed.
