`Python` detection algorithm. This code builds an equivalent width spectrum over 400 pixel wide boxes ($\sim$12Å for 0.03$\AA$ pixel$^{-1}$) blueward of the quasar’s Ly$\alpha$ emission and flags regions of the spectra where the observed equivalent width exceeds the sub-DLA definition (i.e. $N_{{\rm H}\,{\sc \rm I}}\gtrsim10^{19}$ cm$^{-2}$). This candidate list of DLAs and sub-DLAs is further supplemented by visual inspection done by TZ and CP. The DLAs and sub-DLAs have been confirmed by looking for associated metal lines and/or higher members of the Lyman series. This resulted in 150 DLAs/sub-DLAs with $1.6<z_{\rm abs}<4.7$ for which Ly$\alpha$ is covered in the spectra of these quasars. This method is complete down to the sub-DLA definition of $N_{{\rm H}\,{\sc \rm I}}=10^{19}$ equivalent to $\rm EW_{\rm rest}=2.5$$\AA$ based on a curve of growth analysis [@dessauges03].

$N_{{\rm H}\,{\sc \rm I}}$ measurements of DLAs and sub-DLAs
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An extensive search in the literature was undertaken to identify which of these damped absorbers were already known. Of the 150 DLAs/sub-DLAs that we have identified above, 131 (87 DLAs and 44 sub-DLAs) have their $N_{{\rm H}\,{\sc \rm I}}$ already reported in the literature. Of the remaining 19 (6 DLAs and 13 sub-DLAs), 10 (3 DLAs and 7 sub-DLAs) are 