  Boson Sampling represents a promising witness of the supremacy of quantum
systems as a resource for the solution of computational problems. The classical
hardness of Boson Sampling has been related to the so called
Permanent-of-Gaussians Conjecture and has been extended to some generalizations
such as scattershot Boson Sampling, approximate and lossy sampling under some
reasonable constraints. However, it is still unclear how demanding these bounds
are for a quantum experimental sampler. Starting from a state of the art
analysis and focusing on the foreseeable practical conditions needed to reach
quantum supremacy, we look at different techniques and present a more general
and effective solution. We apply our approach to both the experimental
suggestions presented to date and we eventually find in both cases a new
threshold that is less error sensitive and experimentally more feasible.
