Universal Sets and Cover-Free Families

Abstract

We propose a polynomial time construction of an $(n,d)$-universal set over alphabet $\Sigma =\{0,1\}$, of size $d\cdot 2^{d+o(d)}\cdot \log n$. This is an improvement over the size, $d^5{2}^{2.66d}\log n$, of an $(n,d)$-universal set constructed by Bshouty, \cite{BshoutyTesters}, over alphabet $\Sigma =\{0,1\}$.