  Let || . || be a norm on R^n. Averaging || (\eps_1 x_1, ..., \eps_n x_n) ||
over all the 2^n choices of \eps = (\eps_1, ..., \eps_n) in {-1, +1}^n, we
obtain an expression ||| . ||| which is an unconditional norm on R^n.
  Bourgain, Lindenstrauss and Milman showed that, for a certain (large)
constant \eta > 1, one may average over (\eta n) (random) choices of \eps and
obtain a norm that is isomorphic to ||| . |||. We show that this is the case
for any \eta > 1.
