The creation or preservation, of 200,000 below-market-rate apartments over the next decade was one of Bill de Blasio’s key populist propositions during his campaign. The trick is how to accomplish this rather socialist notion of charging rents according to the renter’s ability to pay. Enter the tallness tax: You can build up, up, up, but in return you have to stock your high-rise with some income-restricted units. The redevelopment of the Domino Sugar Factory on the Williamsburg waterfront is a case in point: The developer, Two Trees, wanted to build taller (and more architecturally swaggering) towers than the city had originally approved. In return, Two Trees agreed to add 40 units, so that about 700 of the total 2,300 will be “affordable.” Which means that people who make between $20,109 and $24,080 can qualify for a brand-new studio for as little as $553 per month. But: only if they enter and win a lottery for the apartments. Getting a cheap apartment is always a little about luck.