For a hypergraph $H$, the transversal is a subset of vertices whose intersection with every edge is nonempty. The cardinality of a minimum transversal is the transversal number of $H$, denoted by $\tau(H)$. The Tuza constant $c_k$ is defined as $\sup{\tau(H)/ (m+n)}$, where $H$ ranges over all $k$-uniform hypergraphs, with $m$ and $n$ being the number of edges and vertices, respectively. We give an upper bound and a lower bound on $c_k$. The upper bound improves the known ones for $k\geq 7$, and the lower bound improves the known ones for $k\in\{7, 8, 10, 11, 13, 14, 17\}$.

翻译：对于超图$H$，横贯是指与每条边都有非空交点的顶点子集。最小横贯的基数称为$H$的横贯数，记为$\tau(H)$。Tuza常数$c_k$定义为$\sup{\tau(H)/(m+n)}$，其中$H$取遍所有$k$-一致超图，$m$和$n$分别表示边数和顶点数。我们给出了$c_k$的上界和下界。上界改进了$k\geq 7$时的已知结果，下界改进了$k\in\{7, 8, 10, 11, 13, 14, 17\}$时的已知结果。