  We estimate the upper limit redshifts of known FRBs using the dispersion
measure (DM) - redshift ($z$) relation and derive the upper limit peak
luminosity $L_p$ and energy $E$ of FRBs within the observational band. The
average $z$ upper limits range from 0.17 to 3.10, the average $L_p$ upper
limits range from $1.24 \times 10^{42} \rm erg \ s^{-1}$ to $7.80 \times
10^{44} \rm erg \ s^{-1}$, and the average $E$ upper limits range from $6.91
\times 10^{39}$ erg to $1.94 \times 10^{42}$ erg. FRB 160102 with DM $=2596.1
\pm 0.3 \ {\rm pc \ cm^{-3}}$ likely has a redshift greater than 3. Assuming
that its intrinsic DM contribution from the host and FRB source is ${\rm
DM_{host}+DM_{scr}}\sim 100 \ {\rm pc \ cm^{-3}}$, such an FRB can be detected
up to $z \sim 3.6$ by Parkes and by FAST under ideal conditions up to $z \sim
10.4$. Assuming that there exist FRBs detectable at $z\sim 15$ by sensitive
telescopes such as FAST, the upper limit DM for FRB searches may be set to
$\sim 9000 \ {\rm pc \ cm^{-3}}$. For single-dish telescopes, those with a
larger aperture tend to detect more FRBs than those with a smaller aperture if
the FRB luminosity function index $\alpha_{\rm L}$ is steeper than 2, and vice
versa. In any case, large-aperture telescopes such as FAST are more capable of
detecting high-$z$ FRBs, even though most of FRBs detected by them are still
from relatively low redshifts.
