  Let $G$ be a finite permutation group on $\Omega.$ An ordered sequence
$(\omega_1,\dots, \omega_t)$ of elements of $\Omega$ 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.
