Abstract: The covariant lattice formalism provides a consistent method for the construction of chiral four-dimensional heterotic string vacua. In this talk I present a classification of this corner of the string landscape which uses the theory of genera of quadratic forms. A lower bound on the number of these models is then obtained from the Smith-Minkowski-Siegel mass formula. I then talk in detail about the enumeration of two rather small genera of N=1 supersymmetric models, and about the phenomenology of an explicit model.