5 problems

Let $k$ and $\lambda$ be fixed positive integers with $k\geqslant \lambda+1$. Let $(X,\mathcal B)$ be a cyclic $(v,k,\lambda)$-BIBD with $v\geqslant v_0$, where $v_0$ is an integer…

Existence conjecture. For each D-optimal parameter set $(v;r,s;\lambda)$ there exists a difference family over some abelian group of order $v$ having these parameters.

Symmetry-symbol conjecture. For each normalized and non-exceptional PPS $(v;k_1,k_2,k_3,k_4;\lambda)$ there exist PDFs with symmetry symbols $(s{**})$ and $({**}s)$.

Let $(V,\mathcal{B})$ be a cyclic $(v,k,1)$-design: the blocks are partitioned into orbits under a cyclic automorphism, and a base block is one chosen block from each orbit. Disjoi…

Complementary exceptional propus-parameter conjecture. In positive integers, this equation has a unique solution $(a,b)$ satisfying $1<a\le(s-1)/2$; moreover, $a-b$ is either a squ…