Blocking Sets of Index Three

TL;DR

This paper clarifies the characterization of blocking sets of index three in projective planes, providing constructions for Rédéi blocking sets and explicitly classifying all such sets in PG(2,7).

Contribution

It offers new constructions for Rédéi blocking sets of index three and fully classifies these sets in PG(2,7), enhancing understanding of their structure.

Findings

Constructed all Rédéi blocking sets of index three in PG(2,q).

Explicit classification of blocking sets of index three in PG(2,7).

Clarified existing literature statements about these blocking sets.

Abstract

In this note we will provide proofs for the various statements that have been made in the literature about blocking sets of index three. Our aim is to clarify what is known about the characterization of these sets. Specifically, we provide constructions for all R\'edei blocking sets in PG(2,q) of index three and explicitly determine all blocking sets of index three in PG(2,7).