Small blocking sets in higher dimensions (Q5940304)

Let \(B\) be a minimal blocking set of \(PG(n,q)\), \(q=p^h\), with respect to \(k\)-dimensional subspaces, and with \(|B|<\frac 32(q^{n-k}+1)\).NEWLINENEWLINENEWLINEThe authors show that if \(k = n - 1\), the case of hyperplanes, then \(B\) intersects every hyperplane in \(1\bmod p\) points. Moreover, for any \(k\), including \(k=n-1\), let \(p>2\), then they establish that any subspace that intersects \(B\) will do so in \(1\bmod p\) points. Among other things, they also determine possible sizes of small minimal blocking sets with respect to \(k\)-dimensional subspaces.