An improved upper bound in the maximum dispersal problem

For integral? m?2, let x₁,…, x_m be any unit vectors in R_n, the real Euclidean space of n dimensions. We obtain an upper bound for the quantity min_i≠j|x_i-x_j| which, though not as simple, is uniformly sharper than one recently obtained by the author. The result has application to the so-called maximum-dispersal problem, an open problem recently popularized by Klee.