NEC4.2 provides some information about this topic that may be of interest to some readers.
The number of horizontal radial wires used in an elevated "counterpoise" can be far fewer than the 120 buried wires used by most AM broadcasters, and the even fewer numbers of buried wires often used with vertical monopoles, inverted Ls etc by amateur radio operators.
Several AM broadcast stations use 3 or 4 pairs of λ/4, co-linear, horizontal radial wires installed 10-15 feet above the earth, spaced equally from each other.
Monopoles using such elevated radials can have elevation pattern peak directivity and measured radiation efficiency about equal to that when using 120 x λ/4 buried radials (other things equal). Wire conductors connecting the antenna system to the earth are neither needed nor used to achieve this performance.
This is true because the source of the r-f current flowing on elevated radials is a direct, wire path through the 2nd conductor of the transmission line to/from the transmitter. The source of r-f current flowing on buried radials is the r-f current flowing in the surface of the earth within λ/2 of the base of the monopole, as the result of its radiation -- which necessarily must travel through a lossy conductor (Earth) to reach those radials.
The reason such broadcast stations installed elevated radials is almost always related to the nature of the earth at the transmit site -- typically too rocky to permit using buried radials.
Below is a NEC4.2 comparison of the patterns/directivities of a λ/4 monopole for the configurations and conditions shown there.
Added March 4, 2020:
Another analysis of this is shown in the more recently done study/graphic below.
Note that the performance of these antenna systems when installed at sites with relatively poor Earth conductivity is fairly similar.