On Exact Minimal \((1,5)\)-Covers of Thirteen Points

In “On the exact minimal (1, 4)-cover of twelve points” (\textit{Ars Combinatoria} 27, 3–18, 1989), Sane proved that if \(E\) is an exact minimal (1, 5)-cover of nineteen points, then \(E\) has 282, 287, 292, or 297 blocks. Here we rule out the first possibility.