Abstract For each d ≥ 2, we give the construction of a sequence (νdn)n>o of sets of (d+l)n points of diameter 1 in Download : Download full-size image d, such that a unit ball cannot contain more than 1 (d + 1) ∣ν n ∣ + 1 points. In the case d=2, this answers a conjecture of McDiarmid.