Low-dimensional irreducible rational representations of classical algebraic groups

Let $G$ be an algebraic group of classical type of rank $l$ over an algebraically closed field $K$ of characteristic $p$. We list and determine the dimensions of all irreducible $KG$-modules $L$ with $\dim L<\left(\genfrac{}{}{0px}{}{l+1}{4}\right)$ if $G$ is of type $A_l$, and with $\dim L<16\left(\genfrac{}{}{0px}{}{l}{4}\right)$, if $G$ is of type $B_l$, $C_l$ or $D_l$.