  We present constraints on the amplitude of local Primordial Non-Gaussianities
(PNG), $f_{\rm NL}$, using the quasar sample in the Sloan Digital Sky Survey IV
extended Baryon Oscillation Spectroscopic Survey Data Release 16. We analyze
the power spectrum monopole, testing for the presence of scale dependent galaxy
bias induced by local PNG. Our analysis makes use of optimal redshift weights
that maximize the response of the quasar sample to the possible presence of non
zero PNG. We find $-4<f_{\rm NL}<27$ at $68\%$ confidence level, which is among
the strongest bounds with Large Scale Structure data. The optimal analysis
reduces the error bar by about 10% compared to the standard one, an amount
which is smaller than what was expected from a Fisher matrix analysis. This,
and the reduced improvement over previous releases of the same catalog, suggest
the presence of still unknown systematic effects in the data. If the quasars
have a lower response to local PNG, our optimal constraint becomes $-23<f_{\rm
NL}<21$ at $68\%$, with an improvement of $30\%$ over standard analyses. We
also show how to use the optimal weights to put data-driven priors on the
sample's response to local PNG.
