Under the provisions of this subchapter, the board may lease to any person for the production of oil and natural gas:
(1) islands, saltwater lakes, bays, inlets, marshes, and reefs owned by the state within tidewater limits;
(2) the portion of the Gulf of Mexico within the jurisdiction of the state;
(3) all unsold surveyed and unsurveyed public school land; and
(4) all land sold with a reservation of minerals to the state under Section 51.054 or 51.086 of this code in which the state has retained leasing rights.