In a recent paper (Phys. Rev. A 90, 022316 (2014) ), Goyeneche et al. established a link between the combinatorial notion of orthogonal arrays and k-uniform states and present open issue. (B) Find for what N there are 3-uniform states of N-qubits. In this paper, we demonstrate the existence of 3-uniform states of N-qubits for N=11,..,15".
@article{arxiv.1509.09049,
title = {3-Uniform states and orthogonal arrays},
author = {Xin-wei Zha and Irfan Ahmed and Yanpeng Zhang},
journal= {arXiv preprint arXiv:1509.09049},
year = {2015}
}