  Shell-type supernova remnants (SNRs) are considered prime candidates for the
acceleration of Galactic cosmic rays (CRs) up to the knee of the CR spectrum at
$\mathrm{E} \approx \mathrm{3}\times \mathrm{10}^\mathrm{15}$ eV. Our Milky Way
galaxy hosts more than 350 SNRs discovered at radio wavelengths and at high
energies, of which 220 fall into the H.E.S.S. Galactic Plane Survey (HGPS)
region. Of those, only 50 SNRs are coincident with a H.E.S.S source and in 8
cases the very high-energy (VHE) emission is firmly identified as an SNR. The
H.E.S.S. GPS provides us with a legacy for SNR population study in VHE
$\gamma$-rays and we use this rich data set to extract VHE flux upper limits
from all undetected SNRs. Overall, the derived flux upper limits are not in
contradiction with the canonical CR paradigm. Assuming this paradigm holds
true, we can constrain typical ambient density values around shell-type SNRs to
$n\leq 7~\textrm{cm}^\textrm{-3}$ and electron-to-proton energy fractions above
10~TeV to $\epsilon_\textrm{ep} \leq 5\times 10^{-3}$. Furthermore, comparisons
of VHE with radio luminosities in non-interacting SNRs reveal a behaviour that
is in agreement with the theory of magnetic field amplification at shell-type
SNRs.
