  We compute the based rings of two-sided cells corresponding to the unipotent
classes in $Sp_6(\mathbb C)$ with Jordan blocks (33), (411), (222)
respectively. The results for the first two two-sided cells also verify
Lusztig's conjecture on the structure of the based rings of two-sided cells of
an affine Weyl group. The result for the last two-sided cell partially suggests
a modification of Lusztig's conjecture on the structure of the based rings of
two-sided cells of an affine Weyl group.
