  In this paper, we attach several new invariants to connected strongly regular
graphs (excepting conference graphs on non-square number of vertices) : one
invariant called the discriminant, and a p-adic invariant corresponding to each
prime number p. We prove parametric restrictions on quasi-symmetric 2-designs
with a given connected block graph $G$ and a given defect (absolute difference
of the two intersection numbers) solely in terms of the defect and the
parameters of $G$, including these new invariants. This is a natural analogue
of Schutzenberger's Theorem and the Shrikhande-Chowla-Ryser theorem. This
theorem is effective when these graph invariants can be explicitly computed. We
do this for complete multipartite graphs, co-triangular graphs, symplectic
non-orthogonality graphs (over the field of order $2$) and the Steiner graphs,
yielding explicit restrictions on the parameters of quasi-symmetric 2-designs
whose block graphs belong to any of these four classes.
