What is the ruling on purchasing from housing associations affiliated with syndicates that first pay the apartment's share of the land, then determine the remaining amount based on the cost of construction, finishing, and floor, and assign the apartment by public lottery?

A specific ruling cannot be given for the purchase mentioned in the question due to the lack of clarity regarding the nature and terms of the contract. However, in general, if associations collect money from subscribers, purchase land, and construct properties as agents for their members, then it is permissible to distribute the apartments by lottery, provided that these associations adhere to Sharia regulations in their dealings (buying, selling, and manufacturing contracts - istisna'). But if the association is not acting as an agent and instead sells or enters into istisna' contracts, then it is not permissible to contract with it due to the uncertainty (jahalah) of the sold item or the manufactured item.