Small maximal spaces of degenerate matrices

In 1985 Fillmore, Laurie and Radjavi asked whether a maximal linear subspace in the variety of degenerate $N \times N$-matrices can have dimension smaller than $N$. Following the work of J. Draisma, we will show that for infinitely many $N$ there exists an 8-dimensional maximal space in the variety of degenerate $N \times N$-matrices.