The two smallest minimal blocking sets of $\q(2n,3)$, $n \geqslant 3$

Abstract

We describe the two smallest minimal blocking sets of ${\rm Q}(2n,3)$, $n\geqslant 3$. To obtain these results, we use the characterization of the smallest minimal blocking sets of ${\rm Q}(6,3)$, different from an ovoid. We also present some geometrical properties of ovoids of ${\rm Q}(6,q)$, $q$ odd.