Summary of my understanding of this issue.
Elevated radials - ground losses are minimized but they should each be full quarter wavelength with end effect adjustments for resonance. And ends should be insulated.
Radials on the ground. 32 recommended but length not critical as they get detuned by proximity to ground. 120 used by BC band broadcasters. Aim is to overcome ground losses which are bad enough in good agricultural land but are huge on a rocky mountain.
I prefer elevated radials as you need fewer of them, so much quicker to set up. Modeling predicts only small loss (<1db) in efficiency between 3 and 16 if elevated and resonant. I use 3 on 20m.
Modeling also predicts heavy losses from a system using short stray bits of wire strewn around the base of a Ground mounted vertical. Even if they are given a mysterious name. Good on CB verticals but not for real antennas.
This is mostly well covered by the standard handbooks from RSGB and ARRL