Let $f:X\rightarrow Y$ be a morphism of schemes over a field $k$. Can one check that $f$ is [formally smooth][1] using only Artin rings of the form $k^{\prime}\left[t\right]/t^{n}$, where $k^{\prime}$ is also a field?

Considering cuspidal curves one can show that you do at least need arbitrarily large $n$.


  [1]: http://www.math.columbia.edu/~dejong/algebraic_geometry/stacks-git/more-morphisms.pdf