More Heffter Spaces via Finite Fields

Abstract

A $\left(v,k;r\right)$ Heffter space is a resolvable $\left(v_r,b_k\right)$ configuration whose points form a half-set of an abelian group $G$ and whose blocks are all zero-sum in $G$. It was recently proved that there are infinitely many orders $v$ for which, given any pair $\left(k,r\right)$ with $k\ge 3$ odd, a $\left(v,k;r\right)$ Heffter space exists. This was obtained by imposing a point-regular automorphism group. Here, we relax this request by asking for a point-semiregular automorphism group. In this way, the above result is extended also to the case $k$ even.