The GERDA experiment searches for the lepton-number-violating neutrinoless double-β decay of Ge76 (Ge76→Se76+2e-) operating bare Ge diodes with an enriched Ge76 fraction in liquid argon. The exposure for broad-energy germanium type (BEGe) detectors is increased threefold with respect to our previous data release. The BEGe detectors feature an excellent background suppression from the analysis of the time profile of the detector signals. In the analysis window a background level of 1.0-0.4+0.6×10-3 counts/(keV kg yr) has been achieved; if normalized to the energy resolution this is the lowest ever achieved in any 0νββ experiment. No signal is observed and a new 90% C.L. lower limit for the half-life of 8.0×1025 yr is placed when combining with our previous data. The expected median sensitivity assuming no signal is 5.8×1025 yr.