  To more precisely constrain the Equation of State (EOS) of supradense
neutron-rich nuclear matter, future high-precision X-ray and gravitational wave
observatories are proposed to measure the radii of neutron stars (NSs) with an
accuracy better than about 0.1 km. However, it remains unclear what particular
aspects (other than the stiffness generally spoken of in the literature) of the
EOS and to what precision they will be better constrained. In this work, within
a Bayesian framework using a meta-model EOS for NSs, we infer the posterior
probability distribution functions (PDFs) of incompressibility $K_{0}$ and
skewness $J_{0}$ of symmetric nuclear matter (SNM) as well as the slope $L$,
curvature $K_{\rm{sym}}$, and skewness $J_{\rm{sym}}$ characterizing the
density dependence of nuclear symmetry energy $E_{\rm{sym}}(\rho)$,
respectively, from mean values of NS radii consistent with existing
observations and an expected accuracy $\Delta R$ ranging from about 1.0 km to
0.1 km. We found that (1) the $\Delta R$ has little effect on inferring the
stiffness of SNM at suprasaturation densities, (2) smaller $\Delta R$ reveals
more accurately not only the PDFs but also pairwise correlations among
parameters characterizing high-density $E_{\rm{sym}}(\rho)$, (3) a double-peak
feature of the PDF($K_{\rm{sym}}$) corresponding to the strong
$K_{\rm{sym}}-J_{\rm{sym}}$ and $K_{\rm{sym}}-L$ anti-correlations is revealed
when $\Delta R$ is less than about 0.2 km, (4) the high-precision radius
measurement for canonical NSs is more useful than that for massive ones for
constraining the EOS of nucleonic matter around (2-3) times the saturation
density of SNM.
