4 problems

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…

Prime Power conjecture. When $k$ is not a prime power, there is no finite affine plane with $k^2$ vertices.

Let $e\geq 1$ be an integer. A set of type $(m,n)$ in an affine plane is a point set such that every line intersects it in either $m$ or $n$ points, with both values occurring. Rod…

Prime-power conjecture. There exists a finite affine plane of order $n$ if and only if $n$ is a power of a prime.