The dynamic polarization of nuclear spins by photoexcited electrons is studied in a high quality GaAs/AlGaAs quantum well. We find a surprisingly high efficiency of the spin transfer from the electrons to the nuclei as reflected by a maximum nuclear field of 0.9 T in a tilted external magnetic field of 1 T strength only. This high efficiency is due to a low leakage of spin out of the polarized nuclear system, because mechanisms of spin relaxation other than the hyperfine interaction are strongly suppressed, leading to a long nuclear relaxation time of up to 1000 s. A key ingredient to that end is the low impurity concentration inside the heterostructure, while the electrostatic potential from charged impurities in the surrounding barriers becomes screened through illumination by which the spin relaxation time is increased compared to keeping the system in the dark. This finding indicates a strategy for obtaining high nuclear spin polarization as required for long-lasting carrier spin coherence.