Mixed covering arrays are generalizations of orthogonal arrays. A set of t vectors \(\{x_{1},x_{2},\ldots ,x_{t}\}\) with \(x_{i}\in \mathbb {Z}_{g_{i}}^{N},\) \(1\leqslant i\leqslant t,\) is said to be t-qualitatively independent if for every t-tuple \((a_{1},a_{2},\ldots ,a_{t})\) \(\in \mathbb {Z}_{g_{1}}\times \mathbb {Z}_{g_{2}}\times \dots \times \mathbb {Z}_{g_{t}},\) there exists an integer \(1\leqslant r\leqslant N\) such that \((x_{1}[r],x_{2}[r],\ldots ,x_{t}[r])=(a_{1},a_{2},\ldots ,a_{t})\) . Let \(H=(V(H),E(H))\) be a weighted hypergraph with \(V(H)=\{v_{1},v_{2},\ldots ,v_{k}\}\) and weights \(w(v_{i})=g_{i}, 1\leqslant i \leqslant k\) . A mixed covering array on H, denoted by MCA \((N;H, \prod _{i=1}^{k}g_{i}),\) is an \(N\times k\) array such that column i corresponds to vertex \(v_{i}\in V(H)\) with weight \(g_{i}\) ; the entries in column i are from \(\mathbb {Z}_{g_{i}}\) ; if \(e=\{v_{1},v_{2},\ldots ,v_{t}\}\in E(H),\) the columns correspond to vertices \(v_{1},\) \(v_{2},\) \(\ldots ,\) \(v_{t}\) are t-qualitatively independent. In this paper, we introduce some basic hypergraph operations. As their applications, we provide constructions for optimal mixed covering arrays on some 3-uniform or 4-uniform hypergraphs.
