Projective kk-arcs and 22-level secret-sharing schemes

Motivated by applications to $2$-level secret sharing schemes, we investigate $k$-arcs contained in a $(q + 1)$-arc $\Gamma$ of $\mathrm{PG}(3, q)$, $q$ even, which have only a small number of focuses on a real axis of $\Gamma$. Doing so, we also investigate hyperfocused and sharply focused arcs contained in a translation oval of $\mathrm{PG}(2,q)$