Greedy base sizes for sporadic simple groups

A base for a permutation group G acting on a set Ω is a sequence ℬ of points of Ω such that the pointwise stabiliser G_ℬ is trivial. Denote the minimum size of a base for G by b(G) There is a natural greedy algorithm for constructing a base of relatively small size; denote by 𝒢(G) the maximum size of a base it produces. Motivated by a longstanding conjecture of Cameron, we determine 𝒢(G) for every almost simple primitive group G with socle a sporadic simple group, showing that 𝒢(G) = b(G) .