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.
Highlights
If an affine blocking set B in a non-desarguesian plane of order q contains a line, it is easy to see that B contains at least 2q − 1 points
Little is known about the smallest affine blocking sets, especially when compared to the knowledge about small blocking sets in projective planes
The dual of an affine blocking set, is a set of lines in the dual of Π, covering all the points but one
Summary
If an affine blocking set B in a non-desarguesian plane of order q contains a line, it is easy to see that B contains at least 2q − 1 points. Without the assumption that the blocking set contains a line, the bound from Theorem 2 cannot be generalised to non-desarguesian affine planes. Blocking set of an affine plane of order q, q 25, contains at least
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