  In the covariant lattice formalism, chiral four-dimensional heterotic string
vacua are obtained from certain even self-dual lattices which completely
decompose into a left-mover and a right-mover lattice. The main purpose of this
work is to classify all right-mover lattices that can appear in such a chiral
model, and to study the corresponding left-mover lattices using the theory of
lattice genera. In particular, the Smith-Minkowski-Siegel mass formula is
employed to calculate a lower bound on the number of left-mover lattices. Also,
the known relationship between asymmetric orbifolds and covariant lattices is
considered in the context of our classification.
