IBIS soluble linear groups

Let $G$ be a finite permutation group on $\mathrm{\Omega }\mathrm{.}$ An ordered sequence $({\omega }_1,\dots ,{\omega }_t)$ of elements of $\mathrm{\Omega }$ is an irredundant base for $G$ if the pointwise stabilizer is trivial and no point is fixed by the stabilizer of its predecessors. If all irredundant bases of $G$ have the same cardinality, $G$ is said to be an IBIS group. In this paper we give a classification of quasi-primitive soluble irreducible IBIS linear groups, and we also describe nilpotent and metacyclic IBIS linear groups and IBIS linear groups of odd order.