Definition: Given an independent generating sequence $s=(s_1,...,s_m)$ for a finite group $G$, $s$ is said to satisfy the replacement property if for any nontrivial element $g\in G$, there is a slot $i$-th in $s$ so that $g$ can replace $g_i$ to give a new generating (not necessary independent) sequence for $G$.
$G$ is said to satisfy the replacement property if for all $s$ independent generating sequence of maximal length $m$ (formally noted as $m(G)$), $s$ satisfies the replacement property.
According to a paper by B. Nachman, $PSL(2,p)$ with $p$ prime and $m(G)=4$ then $G$ satisfies the replacement property. Also, another proven theorem said that if $ p =\pm 1 mod8$, $m(G) =3$ then G fails the replacement property, that is, there exists an independent generating sequence $s$ of length-3 so that any element in $G$ not in $s$, once replace any slot in $s$, will not give a generating sequence.
I wonder if anybody has worked with this notion and is there any classification for $PSL(2,q)$ in general with respect to this property. Any comments or suggestion is tremendously appreciated!