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It is known that there exists a network, called as the M-network, which isnot scalar linearly solvable but has a vector linear solution for messagedimension two. Recently, a generalization of this result has been presentedwhere it has been shown that for any integer $m\geq 2$, there exists a networkwhich has a $(m,m)$ vector linear solution, but does not have a $(w,w)$ vectorlinear 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, butdoes not have a $(wk,wn)$ fractional linear solution for $w<m$.

On Achievability of an $(r,l)$ Fractional Linear Network Code