That is almost the whole truth, but not quite Mikel. What you have calculated is base population. It's worth pointing out that total population is affected by the tax level of a planet. For a newly found planet, the tax level is 0% so the population modifier is 1.15 times the base population. So the minimum number of flats to secure a 10 x 10 planet is actually 203.
(Note that credit for this knowledge goes to Ellias Aubec and his fantastic super calculator which tells you all these things.)
Because if you have 203 flats, the BP = (Ln (203) * (203)^2) + (203) = 219,155
Thus at 0% tax, the total population = 1.15 * 219,155 = 252,028 which is just greater than 250k, the required population to control a 10 x 10 planet.
If you take Mikel's figure of 216 flats, the BP = (Ln (216) * (216)^2) + (216) = 251,005
The total population is actually 1.15 * 251,005 = 288,656 which will of course give control but is much more than required.