Quantum k-Uniform States From Quantum Orthogonal Arrays

The quantum orthogonal arrays define remarkable classes of multipartite entangled states called $k$-uniform whose every reductions to $k$ parties are maximally mixed. We present constructions strength 2 with levels prime power, as well some 3. As a consequence, we give infinite 2-uniform $N$ systems dimension power $d\geq 2$ for arbitrary $N\geq 5$; 3-uniform $N$-qubit 6$ and $N\neq 7,8,9,11$; 7$ 7$.