Table schema:
CREATE TABLE table_name_50 (population INTEGER, official_name VARCHAR, area_km_2 VARCHAR)

Question: What is the lowest population that has Big Hole Tract 8 (south) as the official name, with an area km 2 greater than 27.82?
SQL: SELECT MIN(population) FROM table_name_50 WHERE official_name = "big hole tract 8 (south)" AND area_km_2 > 27.82