Exceptional pseudogeometric graphs with eigenvalue r

A. Neumaier enumerated the parameters of strongly regular graphs with smallest eigenvalue $-m$. As a corollary it is proved that for a positive integer $r$ there exist only finitely many pseudogeometric graphs for $pG_{s-r}(s,t)$ with parameters different from the parameters of the net $pG_{s-r}(s,s-r)$ and from the parameters of the $pG_{s-r}(s,(s-r)(r+1)/r)$ graph complementary to the line graph of a Steiner 2-design ($s$ is a multiple of $r$). In this paper we explicitly specify functions $f(r)$ and $g(r)$ such that for $s>f(r)$ or $t>g(r)$ any pseudogeometric graph for $pG_{s-r}(s,t)$ has parameters of the net $pG_{s-r}(s,s-r)$ or parameters of $pG_{s-r}(s,(s-r)(r+1)/r)$.