  We construct a hypersurface of degree 5 in projective space $\PP^8(\CC)$
which contains exactly 23436 ordinary nodes and no further singularities. This
limits the maximum number $\mu_{8}(5)$ of ordinary nodes a hyperquintic in
$\PP^8(\CC)$ can have to
  $23436 \leq \mu_{8}(5) \leq 27876$. Our method generalizes the approach by
the $3^{\text{rd}}$ author for the construction of a quintic threefold with 130
nodes in an earlier paper.
