  An irredundant base $B$ for a permutation group $G\leq \mathrm{Sym}(\Omega)$
is an ordered subset of $\Omega$ with trivial stabiliser such that no base
point is fixed by the stabiliser of its predecessors. Groups whose irredundant
bases all have the same size are termed Irredundant Bases of Invariant Size
(IBIS) groups, and were introduced by Cameron and Fon-Der-Flaass. In this
paper, we contribute to the classification of primitive IBIS groups by
classifying those that are almost simple with sporadic socle.
