# Computing skew left braces of small orders

## TL;DR

This paper enhances an existing algorithm to compute all non-isomorphic skew left braces, enumerates structures up to order 868, and proposes new conjectures based on the data.

## Contribution

It improves an algorithm for computing skew left braces and provides extensive enumeration data up to order 868, facilitating future research.

## Key findings

- Enumerated skew left braces up to order 868
- Proposed new conjectures based on enumeration data
- Enhanced algorithm for computing non-isomorphic skew left braces

## Abstract

We improve Algorithm 5.1 of [Math. Comp. {\bf 86} (2017), 2519-2534] for computing all non-isomorphic skew left braces, and enumerate left braces and skew left braces of orders up to 868 with some exceptions. Using the enumerated data, we state some conjectures for further research.