  We consider a discrete model of euclidean quantum gravity in four dimensions
based on a summation over random simplicial manifolds. The action used is the
Einstein-Hilbert action plus an $R^2$-term. The phase diagram as a function of
the bare coupling constants is studied in the search for a sensible continuum
limit. For small values of the coupling constant of the $R^2$ term the model
seems to belong to the same universality class as the model with pure
Einstein-Hilbert action and exhibits the same phase transition. The order of
the transition may be second or higher. The average curvature is positive at
the phase transition, which makes it difficult to understand the possible
scaling relations of the model.
