2-blocking sets in PG(4, \(q\)), \(q\) square
Let \(PG(N, q)\) be the projective space of dimension \(N\) over the finite field \(GF(q)\). A 2-blocking set \(B\) in \(PG(N, q)\) with \(N \geq 3\) is a set \(B\) of points such that any \((N-2)\)-dimensional subspace intersects \(B\). The authors prove the following result: Suppose \(B\) is a minimal 2-blocking set of \(PG(N,q)\), \(N \geq 4\), \(q\) a square and \(q > 9\). If \(|B |\leq q^2 + q \sqrt{q} + q + \sqrt{q} + 1\), then either \(B\) is the point set of a plane or \(B\) is a cone over a Baer subplane or \(B\) is the point set of a subgeometry \(PG(4,\sqrt{q})\). For \(q = 4\) and \(q=9\), the problem remains open.
scientific article; zbMATH DE number 1428676