5 problems

Let $G$ be a partial geometry with parameters $(s,t,\alpha)$ as in the paper, where $d=2^i\ge 2$ and $d'=2^j\ge 2$, and let $\mathcal{P}$ be a projective plane of order $q=2^{i+j}$…

Let $G$ be a partial geometry with parameters $(s,t,\alpha)$ as in the paper, for integers $d\ge 2$ and $d'\ge 2$, and let $q=dd'$. Suppose that $G$ arises from a maximal arc of de…

Power-of-2-or-3 conjecture. If $\mathcal{S}$ is a $pg(s,t,\alpha)$ of rigid type, then

Mixed-type nonexistence conjecture. Partial geometries of mixed type with $\alpha=2$ do not exist.

MMS star conjecture. For any nonnegative weighting, the largest MMS set has size at least the size of a star.