  A difference set is said to have classical parameters if $ (v,k, \lambda) =
(\frac{q^d-1}{q-1}, \frac{q^{d-1}-1}{q-1}, \frac{q^{d-2}-1}{q-1}).$ The case
$d=3$ corresponds to planar difference sets. We focus here on the family of
abelian difference sets with $d=4$. The only known examples of such difference
sets correspond to the projective geometries $PG(3,q)$. We consider an
arbitrary difference set with the parameters of $PG(3,q)$ in an abelian group
and establish constraints on its structure. In particular, we discern embedded
substructures.
