Vector packing in finite dimensional vector spaces

AbstractLet m be an integer ⩾ 2. The effect of crowding m unit vectors x1,…,xm into the real Euclidean space Rn of n dimensions is investigated. In particular, several upper bounds for the quantity mini≠j∥xi − xj∥ 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