  The E6 grand unified theory is an attractive candidate intermediate theory
between the standard model and string theory. However, only one E6 grand
unified model with three generations and at least one adjoint Higgs field has
been derived from string theory in the literature, and this model is
phenomenologically unsatisfactory. Recently, in arXiv:1012.1690, we have
constructed two new such E6 grand unified models in heterotic asymmetric
orbifolds. Although our new models themselves cannot resolve the unsatisfactory
point in the previous model, our discovery raises hopes that one can construct
many other such models in this framework and find better models. Here, by
giving partition functions explicitly, we explain the details of our
construction. Utilizing the lattice engineering technique and the diagonal
embedding method, we can construct models systematically. We hope that these
techniques and the details of our construction will lead to more
phenomenologically desirable models.
