Avogadro as we know it is not a fractional approximation

 I  know (3/2)^(109 + 27) get me Avogadro's, or very close.

108 is the maximum number of approximation to an irrational;.

Avogadro is measured with energy input,  it is flat earth. It is not the natural vacuum so are not self sampled, hence they get the extra 37 index spots.  So we have two constants, the energy equalized version and the under sampled version. 

Doing Avogadro is adding hard barriers and forcing collisions. The count of electrons assumes the electrons are a Gaussian blob. They have it in a positive spherical shell and are cooling it down.    They can read out the charge count.   The experiment is energy consuming.