  We consider "magnetized brane" compactifications of the type I/heterotic
string on K3 with U(1) background fluxes. The nonabelian gauge group and matter
content of the resulting six-dimensional vacua are parameterized by a matrix
encoding a lattice contained within the even, self-dual lattice Gamma^{3,19}.
Mathematical results of Nikulin on lattice embeddings make possible a simple
classification of such solutions. This approach makes it possible to explicitly
and efficiently construct models in this class with a particular allowed gauge
group and matter content, so that one can immediately "dial-a-model" with
desired properties.
