# Groups Obtained from $2-(n,4,3)$ Supersimple Designs

## TL;DR

This paper advances the classification of Conway groupoids linked to 2-(n,4,3) supersimple designs by improving bounds on hole stabilizers and providing partial classifications.

## Contribution

It improves bounds for hole stabilizers to be primitive or contain the alternating group, aiding the classification of Conway groupoids for specific parameters.

## Key findings

- Bounds for hole stabilizers are improved.
- Partial classification achieved for lambda=3.
- Enhanced understanding of group actions in design theory.

## Abstract

We contribute towards the classification programme for Conway groupoids associated to a $2-(n,4,\lambda)$ design. Our main results improve the known bounds for a hole stabilizer to be primitive, or to contain the alternating group, ${\rm Alt}(n-1)$. We exploit these improved bounds to give a partial classification for Conway groupoids when $\lambda=3$.