Primitive permutation IBIS groups

Let G be a finite permutation group on Ω. An ordered sequence of elements of Ω, (ω1,…,ωt), is an irredundant base for G if the pointwise stabilizer G_(ω1,...,ωt) is trivial and no point is fixed by the stabilizer of its predecessors. If all irredundant bases of G have the same size we say that G is an IBIS group. In this paper we show that if a primitive permutation group is IBIS, then it must be almost simple, of affine-type, or of diagonal type. Moreover we prove that a diagonal-type primitive permutation groups is IBIS if and only if it is isomorphic to PSL(2,2f)×PSL(2,2f) for some f≥2, in its diagonal action of degree 2f(22f−1).