7 problems

Let a KM-arc of type $t$ be contained in a projective plane, let $\ell$ be a given $t$-secant, and let the $t$-nucleus be the common point of the $t$-secants. An $\mathbb{F}_2$-lin…

Let $q$ be a prime power, and let $\mathcal{L}$ denote the linear set constructed in the paper in $\operatorname{PG}(1,q^6)$. A linear set is maximum scattered if it is scattered a…

Szőnyi's conjecture. The blocking set $B$ has at least

Maximal affine-set linearity conjecture. If $t=s>2$, then $\mathcal{U}$ is an affine $\operatorname{GF}(s)$-linear set.

Let $\pi$ be an order-$q$ subplane in ${\rm PG}(2,q^3)$ with exterior line $\ell$. Let $\mathscr S$ be the set of projections of $\pi$ from points…

Small minimal blocking set linearity conjecture. Every small minimal blocking set should be an $\mathbb{F}_q$-linear set.

Let $q=p^t$ be a prime power, and let $B$ be a small minimal blocking set in $\mathrm{PG}(n,q)$, meaning that $B$ meets every hyperplane, satisfies $|B|<3(q+1)/2$, and has no prope…