A New Infinite Family of Hemisystems of the Hermitian Surface

Abstract

In this paper, we construct an infinite family of hemisystems of the Hermitian surface $\mathsf{H}(3,q^2)$. In particular, we show that for every odd prime power $q$ congruent to $3$ modulo $4$, there exists a hemisystem of $\mathsf{H}(3,q^2)$ admitting $C_{(q^3+1)/4}:C_3$.

Fixed typos, added open problems section

References in corpus (1)

• A new family of tight sets in ${\mathcal{Q}}^{+}(5,q)$