Publication of the list of delinquencies and notice shall be made in the newspaper designated by the board. If assessments are not payable in installments, the designation of the newspaper shall be made by the board on or before the fifteenth day of December of the year in which the assessment was levied. If assessments are payable in two installments, the designation shall be made by the board on or before the fifteenth day of June following the year in which the assessment was levied. If the designation is not made by the board within the time provided in this section, the collector shall select the newspaper.