  Compactifications of heterotic theories on smooth Calabi-Yau manifolds
remains one of the most promising approaches to string phenomenology. In two
previous papers, http://arXiv.org/abs/arXiv:1106.4804 and
http://arXiv.org/abs/arXiv:1202.1757, large classes of such vacua were
constructed, using sums of line bundles over complete intersection Calabi-Yau
manifolds in products of projective spaces that admit smooth quotients by
finite groups. A total of 10^12 different vector bundles were investigated
which led to 202 SU(5) Grand Unified Theory (GUT) models. With the addition of
Wilson lines, these in turn led, by a conservative counting, to 2122 heterotic
standard models. In the present paper, we extend the scope of this programme
and perform an exhaustive scan over the same class of models. A total of 10^40
vector bundles are analysed leading to 35,000 SU(5) GUT models. All of these
compactifications have the right field content to induce low-energy models with
the matter spectrum of the supersymmetric standard model, with no exotics of
any kind. The detailed analysis of the resulting vast number of heterotic
standard models is a substantial and ongoing task in computational algebraic
geometry.
