  The well-known absolute bound condition for a primitive symmetric association
scheme (X,S) gives an upper bound for |X| in terms of |S| and the minimal
non-principal multiplicity of the scheme. In this paper we prove another upper
bounds for |X| for an arbitrary primitive scheme (X,S). They do not depend on
|S| but depend on some invariants of its adjacency algebra KS where K is an
algebraic number field or a finite field.
