S.D. Codified Laws § 5-3-3
The commissioner of school and public lands is authorized and directed to ascertain and locate the general grants of land made by Congress to this state and when such commissioner shall find that sections sixteen and thirty-six or any part thereof, in any township of the state, were sold or otherwise disposed of by or under the authority of any act of Congress prior to the admission of the state into the union, then such commissioner shall, by and with the approval of the secretary of the interior or the secretary of agriculture, when necessary, select from the surveyed, unreserved, and unappropriated lands of the United States within the limits of this state, other land equivalent thereto in area and value, in legal subdivisions of not less than one-quarter section if possible, and as contiguous as may be to the section in lieu of which the same is taken.
SDCL 5-3-3