  $ $Abert, Gelander and Nikolov [AGN17] conjectured that the number of
generators $d(\Gamma)$ of a lattice $\Gamma$ in a high rank simple Lie group
$H$ grows sub-linearly with $v = \mu(H / \Gamma)$, the co-volume of $\Gamma$ in
$H$. We prove this for non-uniform lattices in a very strong form, showing that
for $2-$generic such $H$'s, $d(\Gamma) = O_H(\log v / \log \log v)$, which is
essentially optimal. While we can not prove a new upper bound for uniform
lattices, we will show that for such lattices one can not expect to achieve a
better bound than $d(\Gamma) = O(\log v)$.
