Good day,
The Min. BER is the lowest calculated BER for the eye based on an optimized decision instant (time at which the decision is made) and optimized threshold (amplitude of the decision). We basically start from a decision instant of 0 and go all the way to 1 (where 1 = bit period) and calculate the BER assuming varying threshold settings. In other words we map all the BER points within the eye (using statistical calculations at each point) and choose the lowest estimated BER from the set.
We also provide BER calculations based on user-defined threshold and user-defined decision instant (these are included in the results). Cheers!