We have grown high-crystallinity ZnO thin films on lattice-matched ScAlMgO4 substrates by pulsed-laser deposition with doping donor (Ga) and acceptor (N) simultaneously. Alternating ablation of ceramics with concentrated Ga addition and highly pure single crystal targets yielded in a controlled Ga concentration (CGa) in a wide range of 10 18-1020cm-3 with minimal contamination of undesired impurities such as Al and Si. The use of the originally developed temperature-gradient method, where controlled and continuous gradient of the growth temperature is given to the single substrate with a range of about 50-200°C, results in a continuous spread of N concentration (CN) in a controlled fashion. Therefore, the ratio of CN/CGa can be varied continuously in a wide range for each film, assuring that a region satisfying p-type codoping condition predicted by T. Yamamoto and H. K. Yoshida [Jpn. J. Appl. Phys., Part 2 38, L166 (1999)] is included in the sample. The electrical properties were measured for over thousand specimens of lithographically patterned Hall bars without observing any sign of p-type conduction.