So there are some major discrepancy in the estimation of early Qing population. It is not until 1776 that the Qing started to count individual heads in tax, so early Qing census figures mentioning the Ding are just tax units and completely useless in determining its real population.
Cao Shuji gave a much higher estimate of early Qing population than others:
1644: 152.5 million
1679: 160 million
1776: 311.5 million
1820: 383.1 million
This figure is higher than around 120 million given by Ge Jianxiong as the early Qing figure or the even lower traditional estimates of below 100 million.
Cao's methods however, are more scientific, as he extensively used county level gazetteers in the Qing to add up the figures for a population instead of looking just at national census and make assumptions from that. Yet the problem is that he can only really make relatively reliable estimates from 1776 on.
He assumes that the Manchu conquest did not actually result in much of a population decline, most of the late Ming decline was the result of the civil war that happened since the 1630s, and the Manchu takeover of the north was too fast too see any population decline; they did slaughter in the south but only at a few selected places, while the north was growing in population. Even the conquest of the South for the Qing was much more smooth than say the Mongol conquest.
His methods also challenges other theories. According to him, there was no real population explosion under the Qing. Early Qing growth was not faster than those of the Han, Tang, or Song, albeit it was faster than the Yuan and Ming. But for the purpose of this thread, if we use his figures, Qing population was always higher than Mughal population (it would be around 185 million for 1700). Ge Jianxiong's estimates would imply that the two had comparable population, whereas traditional estimates would imply the Qing had less and there was huge population explosion.