  The fusion rules and modular matrix of a rational conformal field theory obey
a list of properties. We use these properties to classify rational conformal
field theories with not more than six primary fields and small values of the
fusion coefficients. We give a catalogue of fusion rings which can arise for
these field theories. It is shown that all such fusion rules can be realized by
current algebras. Our results support the conjecture that all rational
conformal field theories are related to current algebras.
