Maximal partial spreads in \(PG(3,5)\). (Q2715974)

A maximal partial spread \(S\) in \(PG(3,5)\) that is not complete satisfies \(12 \leq s \leq 22\), where \(s = | S| \), by earlier results. The author used computer to find \(S\) for every \(s\) with \(13 \leq s \leq 22\), and to prove that there never is \(s = 12\). The latter computation lasted weeks, and was based on a backtracking algorithm, in which one adds a line per time. The first three lines can be fixed, and the next two (or three) lines have to satisfy at least one of the three additional criteria that follow from the condition \(s = 12\).