  Consider a finite field $\mathbb{F}_q$ and positive integers $d,m,r$ with
$1\leq r\leq \binom{m+d}{d}$. Let $S_d(m)$ be the $\mathbb{F}_q$ vector space
of all homogeneous polynomials of degree $d$ in $X_0,\dots,X_m$. Let $e_r(d,m)$
be the maximum number of $\mathbb{F}_q$-rational points in the vanishing set of
$W$ as $W$ varies through all subspaces of $S_d(m)$ of dimension $r$. Ghorpade,
Datta and Beelen had conjectured an exact formula of $e_r(d,m)$ when $q\geq
d+1$. We prove that their conjectured formula is true when $q$ is sufficiently
large in terms of $m,d,r$. The problem of determining $e_r(d,m)$ is equivalent
to the problem of computing the $r^{th}$ generalized hamming weights of
projective the Reed Muller code $PRM_q(d,m)$. It is also equivalent to the
problem of determining the maximum number of points on sections of Veronese
varieties by linear subvarieties of codimension $r$.
