An asymptotic isoperimetric inequality

For a finite metric space V with a metric rho, let V-n be the metric space in which the distance between (a(1),..., a(n)) and (b(1),...,b(n)) is the sum Sigma(i=1)(n) rho(a(i), b(i)). We obtain an asymptotic formula for the logarithm of the maximum possible number of points in V-n Of distance at least d from a, set of half the points of V-n, when n tends to infinity and d satisfies d much greater than root n.