On the spectrum of sizes of semiovals contained in the Hermitian curve

TL;DR

This paper explores the possible sizes of semiovals within the Hermitian curve, providing new constructions and bounds, including an infinite family of 2-blocking sets, advancing understanding of geometric configurations in finite fields.

Contribution

It introduces new bounds and constructions for semiovals in the Hermitian curve, notably an infinite family of 2-blocking sets, enriching the combinatorial geometry literature.

Findings

Bounds on sizes of semiovals established

Construction of an infinite family of 2-blocking sets

Enhanced understanding of geometric configurations in finite fields

Abstract

Some constructions and bounds on the sizes of semiovals contained in the Hermitian curve are given. A construction of an infinite family of 2-blocking sets of the Hermitian curve is also presented.