IBIS primitive groups of almost simple type

Let G be a finite permutation group on Ω. An ordered sequence (ω₁…,ω₎ of elements of Ω is an irredundant base for G if the pointwise stabilizer is trivial and no point is fixed by the stabilizer of its predecessors. The minimal cardinality of a base is said to be the base size of G. If all irredundant bases of G have the same cardinality, G is said to be an IBIS group. In this paper, we classify the finite almost simple primitive IBIS groups whose base size is at least $6$.