S.D. Codified Laws § 12-12-1
The county auditor charged with the conduct of a primary election shall give notice of any office to be filled by nomination or by declaration and the deadline for filing in all official newspapers in the appropriate district, at least once each week for two consecutive weeks, between the fifteenth and thirtieth day of January in an even-numbered year. A local election official charged with the conduct of a local election shall give notice of any office to be filled by nomination or by declaration and the deadline for filing a nominating petition, in all official newspapers in the locality, at least once each week for two consecutive weeks. The last publication in the notice may not be less than ten nor more than fifteen days before the deadline for filing. The provisions of this section apply unless otherwise provided by law specifically governing the election.
The person in charge of the election shall give further notice of each election stating the date and time of the election, and designating each polling place for the election, in all official newspapers at least once each week for two consecutive weeks, the last publication to be not less than four nor more than ten days before the election. For any runoff election under § 12-6-51.1, one notice shall be published along with a copy of the ballot in each newspaper in the state that publishes on Saturday and Sunday. The secretary of state shall direct the newspapers to publish the ballot and notice on the eleventh or twelfth day after the primary election. The secretary of state shall pay all costs of publication.
SDCL 12-12-1