A small minimal blocking set in \(\mathrm{PG}(n,p^t)\), spanning a \((t-1)\)-space, is linear (Q1952278)

A blocking set in a projective space \(\mathrm{PG}(n,p^t)\) is a set \(B\) of points which intersects every hyperplane. A blocking set is trivial if it contains a line, and it is minimal if no proper subset of it is a blocking set. We say that \(B\) is small if its size is less than \(3(q+1)/2.\) The only known small minimal blocking sets are the linear blocking sets, introduced in the non-quoted papers [\textit{G. Lunardon}, Geom. Dedicata 75, No. 3, 245--261 (1999; Zbl 0944.51004); Combinatorica 21, No. 4, 571--581 (2001; Zbl 0996.51003)], and it has been conjectured that all small minimal blocking sets are linear. In this paper, the authors prove that the conjecture is true if \(B\) spans a \((t-1)-\)subspace.