Notes. Limiting magnitudes corrected for Galactic extinction. We adopted the Dahlen et al. (2005) and Reddy et al. (2008) LFs to relate an absolute magnitude with the knee of a corresponding LF, L_∗: 1.59 < z < 1.9: M_∗ =  −20.69 ± 0.26   mag (U-band), 1.9 ≤ z < 2.7: M_∗ =  −21.01 ± 0.38   mag   (1700   Å), 2.7 ≤ z < 3.4: M_∗ =  −20.84 ± 0.12   mag   (1700   Å). We extended the range of the LFs from z = 1.59 to 1.50 and from z = 3.4 to 3.56, because the change in the M_∗ is smaller than its uncertainty. To compute the absolute magnitude we used M = m − DM(z) + 2.5log (1 + z), where DM(z) is the distance modulus. Different filters than F775W were used if a filter was closer to the central wavelength of the LF than the F775W band. In the column “Fynbo model” we display the limits on the luminosity of DLA galaxies based on the model by Fynbo et al. (2008).