  The orbital diameter of a primitive permutation group is the maximal diameter
of its orbital graphs. There has been a lot of interest in bounds for the
orbital diameter. In this paper we provide explicit bounds on the diameters of
groups of simple diagonal type.
  As a consequence we obtain a classification of simple diagonal groups with
orbital diameter less than or equal to 4. As part of this, we classify all
finite simple groups with covering number and conjugacy width at most 3. We
also prove some general bounds on the covering number and conjugacy width of
groups of Lie type.
