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

Abstract

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.