How to find the number of vectors to sample in Compressed Sensing?

When comparing my MATLAB code to a previously written one, I come across the following formula for the number of vectors to sample:

n = \text{fix}(p * sqrt(2/3*c))) % n - number of vectors to sample , p - number of pixels in the image
% c - compression amount


The resulting number is used as the "Nyquist cut-off frequency" to choose which vectors to sample from the image:

FX = ceil(-n/2:n/2-1)/p*2*pi


Could someone explain to me the first equation? I don't understand where this equation comes from and how it can select the correct number of vectors to sample for a specific compression amount.

I have previously seen the second equation in the following question, but why is the Nyquist cut-off frequency multiplied by $$2 \pi/ p$$? How was this deduced?