Pooling designs with surprisingly high degree of error correction in a finite vector space

TL;DR

This paper introduces a new family of pooling designs based on finite vector spaces that significantly improve error correction capabilities over existing designs, especially in high-dimensional settings.

Contribution

It generalizes Ngo and Du's designs to finite vector spaces, achieving higher error correction with the same number of items and pools.

Findings

Designs have higher error correction than Ngo and Du's designs.

Error-tolerance improves as the dimension of the space increases.

Performance surpasses previous bounds in high-dimensional cases.

Abstract

Pooling designs are standard experimental tools in many biotechnical applications. It is well-known that all famous pooling designs are constructed from mathematical structures by the "containment matrix" method. In particular, Macula's designs (resp. Ngo and Du's designs) are constructed by the containment relation of subsets (resp. subspaces) in a finite set (resp. vector space). Recently, we generalized Macula's designs and obtained a family of pooling designs with more high degree of error correction by subsets in a finite set. In this paper, as a generalization of Ngo and Du's designs, we study the corresponding problems in a finite vector space and obtain a family of pooling designs with surprisingly high degree of error correction. Our designs and Ngo and Du's designs have the same number of items and pools, respectively, but the error-tolerant property is much better than that of Ngo and Du's designs, which was given by D'yachkov et al. \cite{DF}, when the dimension of the space is large enough.