Clique number and ball containment number of unit ball graphs

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 d, such that a unit ball cannot contain more than 1(d + 1)∣νn∣ + 1 points. In the case d=2, this answers a conjecture of McDiarmid.