# Finite Geometry Seminar

•  Friday, 14.15-15.45  •  ELTE Southern building, room 3.607  •  Pázmány P. sétány 1/C  •

# Program of the current semester (2018 Spring)

## Double blocking sets of size $$3q-1$$ in $$\mathrm{PG}(2,q)$$

Feb 23, Tamás Héger

We report on constructions of minimal double blocking sets of size $$3q-1$$ in $$\mathrm{PG}(2,q)$$ for $$q=13$$, $$16$$, $$19$$, $$25$$, $$31$$, $$37$$ and $$43$$. These are particularly interesting when $$q$$ is prime, because in that case, no examples of double blocking sets of size less than $$3q$$ has been known except for $$q=13$$. All of our examples admit two $$(q-1)$$-secants and have been found using a computer. Furthermore, we show that a double blocking set in $$\mathrm{PG}(2,q)$$ of size $$3q-1$$ cannot have three $$(q-1)$$-secants. These results partially prove and disprove some conjectures of R.~Hill from 1984. Joint work with Bence Csajbók.