Small blocking sets in \(PG(2,p^3)\)
A blocking set in a projective plane is a set of points which intersects every line. A blocking set containing a line is called trivial. A blocking set in a plane of order \(q\) is called small if it contains at most \(3(q+1)/2\) points. If a nontrivial blocking set \(B\) in a plane of order \(q\) contains \(q + N\) points, then each line intersects \(B\) in at most \(N\) points, and if this bound is attained then \(B\) is called of Redei type. The author proves that for \(p \geq 7\) every small minimal blocking set in \(PG(2,q^3)\) is of Redei type. A similar result is known to be true for \(r = 2\), whereas for \(r \geq 4\) there are counterexamples.
scientific article; zbMATH DE number 1515346