SU(3) trits of orbifolded E_8 x E_8' heterotic string and supersymmetric standard model

We present $Z_3$ orbifold compactifications of $E_8\times E_8^{\mathrm{\prime }}$ heterotic string with three Wilson lines, resulting to the maximum number of SU(3) factors. Here, all the matter spectrums are in the SU(3) trits($\equiv$ three representations $\mathbf{3},\bar{\mathbf{3}},\mathbf{1}$) of the $SU(3{)}^8$ GUT. Using this information, we show how three family supersymmetric standard models(SSM) can be obtained. Also, the low lying interesting representations(fundamental and adjoint) of $E_6$ and $E_8$ are given in terms of trits, establishing simple criteria for treating these low lying representations of exceptional groups.