  It is known that there exists a network, called as the M-network, which is
not scalar linearly solvable but has a vector linear solution for message
dimension two. Recently, a generalization of this result has been presented
where it has been shown that for any integer $m\geq 2$, there exists a network
which has a $(m,m)$ vector linear solution, but does not have a $(w,w)$ vector
linear solution for $w<m$. This paper presents a further generalization.
Specifically, we show that for any positive integers $k,n,$ and $m\geq 2$,
there exists a network which has a $(mk,mn)$ fractional linear solution, but
does not have a $(wk,wn)$ fractional linear solution for $w<m$.
