  The QED initial state corrections are calculated to the forward-backward
asymmetry for $e^+e^- \rightarrow \gamma^*/{Z^{0}}^*$ in the leading
logarithmic approximation to $O(\alpha^6 L^6)$ extending the known corrections
up to $O(\alpha^2 L^2)$ in analytic form. We use the method of massive on-shell
operator matrix elements and present the radiators both in Mellin-$N$ and
momentum fraction $z$-space. Numerical results are presented for various
energies around the $Z$-peak by also including energy cuts. These corrections
are of relevance for the precision measurements at the FCC$\_$ee.
