  By considering constraints on the dimensions of the Lie algebra corresponding
to the weight one states of Z_2 and Z_3 orbifold models arising from imposing
the appropriate modular properties on the graded characters of the
automorphisms on the underlying conformal field theory, we propose a set of
constructions of all but one of the 71 self-dual meromorphic bosonic conformal
field theories at central charge 24. In the Z_2 case, this leads to an
extension of the neighborhood graph of the even self-dual lattices in 24
dimensions to conformal field theories, and we demonstrate that the graph
becomes disconnected.
