Digital tracking enables telescopes to detect asteroids several times fainter than conventional techniques .
We describe our optimized methodology to acquire , process , and interpret digital tracking observations , and we apply it to probe the apparent magnitude distribution of main belt asteroids fainter than any previously detected from the ground .
All-night integrations with the Dark Energy Camera ( DECam ) yield 95 % completeness at R magnitude 25.0 , and useful sensitivity to R = 25.6 mag when we use an analytical detection model to correct flux overestimation bias .
In a single DECam field observed over two nights , we detect a total of 3234 distinct asteroids , of which 3123 are confirmed on both nights .
At opposition from the Sun , we find a sky density of 697 \pm 15 asteroids per square degree brighter than R = 25.0 mag , and 1031 \pm 23 brighter than R = 25.6 mag .
We agree with published results for the sky density and apparent magnitude distribution of asteroids brighter than R = 23 mag .
For a power law defined by dN / dR \propto 10 ^ { \alpha R } , we find marginally acceptable fits with a constant slope \alpha = 0.28 \pm 0.02 from R = 20 to 25.6 mag .
Better fits are obtained for a broken power law with \alpha = 0.218 \pm 0.026 for R = 20 to 23.5 mag , steepening to \alpha = 0.340 \pm 0.025 for R = 23.5 to 25.6 mag .
The constant or steepening power law indicates asteroids fainter than R = 23.5 mag are abundant , contrary to some previous claims but consistent with theory .