Vector packing in finite dimensional vector spaces

Let m be an integer ? 2. The effect of crowding m unit vectors x₁,…,x_m into the real Euclidean space R_n of n dimensions is investigated. In particular, several upper bounds for the quantity min_i≠j∥x_i ? x_j∥ are obtained. These are simpler than any previously known and, at least in some cases, almost as sharp. The results have application to the so-called maximum-dispersal (or “misanthrope”) problem, an open problem recently popularized by Klee.