A short proof of the existence of designs

TL;DR

This paper presents a concise proof demonstrating the existence of combinatorial designs, improving upon previous bounds and simplifying the proof process.

Contribution

It introduces a shorter, more efficient proof of the existence of designs with improved bounds compared to prior methods.

Findings

Proof is significantly shorter than previous ones

Provides better bounds for the existence of designs

Simplifies the understanding of design existence

Abstract

We give a new proof of the existence of designs, which is much shorter and gives better bounds.