# Enumerating number fields

## TL;DR

This paper develops small models of number fields to improve bounds on their quantity given degree and discriminant constraints.

## Contribution

It introduces a novel approach to model construction that refines existing bounds on the number of number fields.

## Key findings

- Derived tighter bounds for number fields with fixed degree and discriminant
- Constructed explicit small models of number fields
- Enhanced understanding of the distribution of number fields

## Abstract

We construct small models of number fields and deduce a better bound for the number of number fields of given degree and bounded discriminant.