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 } erg s ^ { -1 } to 7.80 \times 10 ^ { 44 } 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 { pc cm ^ { -3 } } likely has a redshift greater than 3 .
Assuming that its intrinsic DM contribution from the host and FRB source is { DM _ { host } + DM _ { scr } } \sim 100 { 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 { 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 _ { 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 .