  Using the newly developed real space vortex-lattice based theory of
superconductivity, we study the maximum superconducting transition temperature
(T_{c}^{\max}) in the iron-based superconductors. We find that all the reported
FeAs superconductors can be divided into two basic classes (c/a=3 and c/a=5/2)
depending on the lattice constants, where a is the Fe-Fe distance in the
xy-plane and c is the Fe-Fe layer distance along the z-axis. Our results
suggest that the former class has a maximum T_{c}^{\max}<60K, while the latter
class has a lower T_{c}^{\max}\leq 40K. Our investigations further indicate
that, in order to enhance T_{c}^{\max} in this family of compounds, new class
of superconductors with a larger ratio of c/a should be synthesized. It is
likely that their T_{c}^{\max} values could be raised into the liquid nitrogen
range (77K) and 100K, supposing the new analogues with c/a=5 (approximately
c>13A, if a=2.750A) and c/a=11 (c>31A) can be experimentally achieved,
respectively. For the new FeSe series, our mechanism predicts that their
T_{c}^{\max} is impossible to exceed 30 K due to a relatively shorter c-axis
lattice constant (c/a=2). Finally, based on the new experimental results
(arXiv:0811.0094 and arXiv:0811.2205), the possible ways to raise the Tc of the
iron-based superconductors into 70 K are also suggested.
