For a comprehensive list, I guess just visit Wikipedia
https://en.wikipedia.org/wiki/Bell_test
Apparently, the MPQ and LMU found up to $6\sigma$ confidence with $P \approx 10^{-9}$ that the results could be described by local hidden variable theory:
https://arxiv.org/abs/1611.04604
Regarding the $16\sigma$, I don't know which source possibly Cirac was referring to...
