  Given a non-abelian finite simple group $G$ of Lie type, and an arbitrary
generating set $S$, it is conjectured by Laszlo Babai that its Cayley graph
$\Gamma (G,S)$ will have a diameter of $(\log |G|)^{O(1)}$. However, little
progress has been made when the rank of $G$ is large. In this article, we shall
show that if $G$ has rank $n$, and its base field has order $q$, then the
diameter of $\Gamma (G,S)$ would be $q^{O(n(\log n + \log q)^3)}$.
