  In this paper, we prove that it is W[2]-hard to approximate k-SetCover within
any constant ratio. Our proof is built upon the recently developed threshold
graph composition technique. We propose a strong notion of threshold graphs and
use a new composition method to prove this result. Our technique could also be
applied to rule out polynomial time $o\left(\frac{\log n}{\log \log n}\right)$
ratio approximation algorithms for the non-parameterized k-SetCover problem
with $k$ as small as $O\left(\frac{\log n}{\log \log n}\right)^3$, assuming
W[1]$\neq$FPT. We highlight that our proof does not depend on the well-known
PCP theorem, and only involves simple combinatorial objects.
