Examples for derandomization via small sample spaces
Here is an example from low degree testing literature: https://www.math.ias.edu/~avi/PUBLICATIONS/MYPAPERS/BSVW03/BSVW03.pdf.

High-level summary: Consider BLR linearity testing algorithm that given oracle access to a function $f:\mathbb{F}^m \rightarrow \mathbb{F}$, first, samples $x,y$ uniformly randomly from $\mathbb{F}^m$ and then tests if $f(x)+f(y)=f(x+y)$ by querying the function at required points. This paper reduces the amount of randomness usage by sampling $y$ from an epsilon-biased set instead of sampling from the entire space.