Light dual multinets of order six in the projective plane

TL;DR

This paper classifies all light dual multinets of order six with a unique line of length at least two and studies their embeddings in projective planes over characteristic zero fields using computational algebraic methods.

Contribution

It provides a complete classification of specific multinets and introduces a computational approach for their embeddings in projective planes.

Findings

Classification of all such multinets of order six

Development of a computational algebraic method for embeddings

Identification of unique line structures in multinets

Abstract

The aim of this paper is twofold: First we classify all abstract light dual multinets of order $6$ which have a unique line of length at least two. Then we classify the weak projective embeddings of these objects in projective planes over fields of characteristic zero. For the latter we present a computational algebraic method for the study of weak projective embeddings of finite point-line incidence structures.