3 problems

Let $q$ be a prime power, and let $S_q(t,k,n)$ denote the collection of $q$-Steiner systems with parameters $t,k,n$. A non-trivial $q$-Steiner system has $n\geq 2k$. Metsch's conje…

Let the constructed residual $q$-Fano plane be the residual $q$-Steiner system described in the paper, and consider whether it can be extended to a $q$-Fano plane. Nonextendability…

Let $n\geqslant 13$ be a prime with $n\equiv 1\pmod 6$. A binary $q$-Steiner system $\mathcal S_2[2,3,n]$ is a collection of $3$-dimensional subspaces of $\mathbb F_2^n$ such that…