The smaller the value of Smin the weaker the pulsar that can be detected. Therefore the larger the aperture of the antenna or the narrower the pulse w.r.t. the pulse period, the weaker the pulsar that can be detected. Note that also the longer integration time and the wider the pre-detection bandwidth the weaker the pulsar that can be detected - but by a factor of a square root - i.e., an increase of 4 in either of these only decreases the weakest signal detectable by a factor of 2. The most effective changes to the receiving system are aperture (bigger is better) and Tsys (lower is better) - which both affect the weakest pulsar signal detectable directly.
The linear factor S/Nmin is the lowest S/N that still provides a solid validation of the result. Professional astronomers require an S/Nmin of around 8 and amateur astronomers should aim for this, but certainly a minimum of 4.
The important thing to remember for amateurs is that the above equation is derived from the laws of physics and represent the ideal theoretical case. Practical implementations are always poorer than this so if a result is obtained which is better than the above equation (and you still want your results to have scientific validity) then it should be regarded as invalid.
All the successful amateur groups/individuals listed on the 'Home' page are in compliance, according to the data they have supplied, with the pulsar radiometer equation.