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Large blocking sets in PG(2,q2)

Affiliation:	1. ELTE Eötvös Loránd University, Department of Computer Science and MTA-ELTE Geometric and Algebraic Combinatorics Research Group, H-1117 Budapest, Pázmány Péter sétány 1/C, Hungary;2. University of Primorska, FAMNIT, SI-6000 Koper, Glagoljaška 8, Slovenia;3. MTA-ELTE Geometric and Algebraic Combinatorics Research Group, H-1117 Budapest, Pázmány Péter sétány 1/C, Hungary;4. Prezi Inc, H-1065 Budapest, Nagymező utca 54-56, Hungary

Abstract:	Minimal blocking sets in $PG (2, q^{2})$ have size at most $q^{3} + 1$ . This result is due to Bruen and Thas and the bound is sharp, sets attaining this bound are called unitals. In this paper, we show that the second largest minimal blocking sets have size at most $q^{3} + 1 - (p - 3) / 2$ , if $q = p$ , $p \geq 67$ , or $q = p^{h}$ , $p > 7$ , $h > 1$ . Our proof also works for sets having at least one tangent at each of its points (that is, for tangency sets).

Keywords:	Finite plane Unital Blocking set
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