6 problems

Let $v,k,\ell\in\mathbb{Z}^+$ satisfy the necessary parameter equation referred to in the source as Equation, and suppose that there exists a symmetric BIBD on $v$ points with bloc…

Let $\mathcal D$ be a $2$-$(v,k,\lambda)$ design with replication number $r$ and $\lambda\geq (r,2\lambda)^2$. An automorphism group of $\mathcal D$ is half-flag-transitive when it…

Paley ETF spark and bender conjecture. The spark of $\Phi_q$ is $((p+1)/2)^s$ and the bender is a $(p^s, ((p+1)/2)^s,\lambda)$-BIBD.

Let $q$ be a prime power, and let a BIBD consist of $q$ copies of a non-Desarguesian affine plane of order $q$. A non-triangular local resolution system is a local resolution syste…

Binder BIBD conjecture. The binder of $\mathcal G(p,\ldots,p)$ is a

A finite projective plane is a $2$-design whose parameters satisfy the projective-plane axioms; its incidence graph is the bipartite graph joining each point to the blocks containi…