A construction of pooling designs with surprisingly high degree of error correction

TL;DR

This paper introduces a new method for constructing pooling designs that significantly improve error correction capabilities, especially for large sets, surpassing existing designs like Macula's.

Contribution

A novel construction method for pooling designs based on finite sets, achieving higher error correction than previous methods.

Findings

Designs have much better error-tolerant properties for large sets.

The new method outperforms Macula's designs in error correction.

Applicable for given numbers of items and pools.

Abstract

It is well-known that many famous pooling designs are constructed from mathematical structures by the "containment matrix" method. In this paper, we propose another method and obtain a family of pooling designs with surprisingly high degree of error correction based on a finite set. Given the numbers of items and pools, the error-tolerant property of our designs is much better than that of Macula's designs when the size of the set is large enough.