  It is known that there exists a multiple-unicast network which has a rate $1$
linear network coding solution if and only if the characteristic of the finite
field belongs to a given finite or co-finite set of primes. In this paper, we
show that for any non-zero positive rational number $\frac{k}{n}$, there exists
a multiple-unicast network which has a rate $\frac{k}{n}$ fractional linear
network coding solution if and only if the characteristic of the finite field
belongs to a given finite or co-finite set of primes.
