[Edit: This side discussion has been split off from topic AMC Gremlin]
Investigating further...
Here is a comparison of displacement effects:
First with a Gradient Material set to transition from RGB 128 to RGB 129 and Displacement set to 100000%
Second is that gradient rendered to a TGA and used as a Displacement map
Third is that gradient rendered to an OpenEXR and used as a Displacement map
The Material is able to calculate an exact value for every pixel between the 128 and the 129 levels, creating a perfectly smooth slope.
The TGA map, as expected, has one stair step from 128 to 129
The EXR has 8 steps. EXR uses a 16 bit floating point format to store values, but it maps our 0-255 range for black to white to -1.0 to +1.0. From what I read about 16-bit floating point numbers, there 1024 possible values between 0 and 1 (and thus, 2048 between -1 and +1) which matches the result above , with 8 steps between our 128 and 129 gray values.
So it seems that A:M is capable of rendering finer displacements, but EXR doesn't store the finer values needed.
According to OpenEXR docs, EXR can have 32-bit floating point data. Maybe there is an easy way to get A:M to write those?