# Non-existence of two types of partial difference sets

## TL;DR

This paper proves that certain types of partial difference sets cannot exist in Abelian groups of order 216, completing the classification of possible parameters for small partial difference sets.

## Contribution

It establishes the non-existence of two specific types of partial difference sets in Abelian groups of order 216, advancing the classification of such sets.

## Key findings

- Proves non-existence of two types of partial difference sets in order 216 groups
- Completes classification for partial difference sets of size up to 100 in Abelian groups
- Provides theoretical results narrowing the search for partial difference sets

## Abstract

In this note we prove the non-existence of two types of partial difference sets in Abelian groups of order 216. This finalizes the classification of parameters for which a partial difference set of size at most 100 exists in an Abelian group.