  We undertake a systematic scan of vector bundles over spaces from the largest
database of known Calabi-Yau three-folds, in the context of heterotic string
compactification. Specifically, we construct positive rank five monad bundles
over Calabi-Yau hypersurfaces in toric varieties, with the number of Kahler
moduli equal to one, two, and three and extract physically interesting models.
We select models which can lead to three families of matter after dividing by a
freely-acting discrete symmetry and including Wilson lines. About 2000 such
models on two manifolds are found.
