  We examine whether a minimal string model possessing the same massless
spectra as the MSSM can be obtained from $Z_4$, $Z_6$ and $Z_8$ orbifold
constructions. Using an anomaly cancellation condition of the target space
duality symmetry, we derive allowable values of a level $k_1$ of U(1)$_Y$ for
the minimal string model on the orbifolds through computer analyses. We
investigate threshold corrections of the gauge coupling constants of SU(3),
  SU(2) and U(1)$_Y$ and examine consistencies of the model with the LEP
experiments. It is found that $Z_4$ and $Z_8$-II can not derive the minimal
string model but $Z_6$-I, $Z_6$-II and $Z_8$-I are possible to derive it with
$13/12
  \leq k_1\leq 41/30$, $16/15\leq k_1\leq 17/12$ and $1\leq k_1\leq 41/21$
respectively. The minimum values of the moduli on unrotated planes are
estimated within the ranges of the levels.
