Blocking sets of small size and colouring in finite affine planes

  • Sandro Rajola
  • Maria Scafati Tallini


Let (S, L) be an either linear or semilinear space and X ⊂ S. Starting from X we define three types of colourings of the points of S. We characterize the Steiner systems S(2, k, ν) which have a colouring of the first type with X = {P}. By means of such colourings we construct blocking sets of small size in affine planes of order q. In particular, from the second and third type of colourings we get blocking sets B with |B| ≤ 2q − 2.