  The Malle-Navarro conjecture relates central block theoretic invariants in
two inequalities. In this paper, we prove the conjecture for the 2-blocks and
the unipotent 3-blocks of the general linear and unitary groups in non-defining
characteristic. Moreover, we show that the conjecture holds for the unipotent
3-blocks of quotients of central subgroups of the special linear and unitary
groups.
