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