  In this article we consider $S$ to be a set of points in $d$-space with the
property that any $d$ points of $S$ span a hyperplane and not all the points of
$S$ are contained in a hyperplane. The aim of this article is to introduce the
function $e_d(n)$, which denotes the minimal number of hyperplanes meeting $S$
in precisely $d$ points, minimising over all such sets of points $S$ with
$|S|=n$.
