__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.