  We study the local geometry of the zero pattern of a weighing matrix
$W(23,16)$. The geometry consists of $23$ lines and $23$ points where each line
contains $7$ points. The incidence rules are that every two lines intersect in
an odd number of points, and the dual statement holds as well. We show that
more than $50\%$ of the pairs of lines must intersect at a single point, and
construct a regular weighted graph out of this geometry. This might indicate
that a weighing matrix $W(23,16)$ does not exist.
