Constraints on the ϵ_ep and n parameter space as imposed by the flux upper limits (grey bands, each limit constitutes one band). For each constraint a source-intrinsic power-law spectrum with index Γ = 2.3 was assumed. Solid and dotted red lines represent the constraints corresponding to the median and lowest value of the flux upper limit distribution, respectively. The blue line indicates the boundary above which CTA might be able to probe the parameter space, assuming a ten times higher sensitivity than H.E.S.S. and taking the lowest flux upper limit as a reference. Additionally, values of ϵ_ep and n for VHE-detected shell-type SNRs are shown, extracted from the publications in Table A.3. For better comparison, these values are rescaled to the canonical total CR energy in SNRs of 10⁵⁰ erg. The dashed and dotted black lines indicate how the median of the distribution shifts if one limits the maximum proton energy to 100 TeV and 20 TeV, respectively. The histograms show the parameter limit distributions in the extreme hadronic- and leptonic-dominated scenarios.