A New Lower Bound for the Size of an Affine Blocking Set

Maarten De Boeck, Geertrui Van de Voorde

Abstract


A blocking set in an affine plane is a set of points $B$ such that every line contains at least one point of $B$. The best known lower bound for blocking sets in arbitrary (non-desarguesian) affine planes was derived in the 1980's by Bruen and Silverman. In this note, we improve on this result by showing that a blocking set of an affine plane of order $q$, $q\geqslant 25$, contains at least $q+\lfloor\sqrt{q}\rfloor+3$ points.

Keywords


Blocking set, Affine blocking set

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