Within five (5) days after the filing of the petition, the county board of election commissioners shall call an election to be held in the city or town at a time not less than thirty (30) days nor more than sixty (60) days from the date of the filing of the petition. The board shall give due notice thereof by publication in some newspaper published in the city or town, weekly for two (2) weeks, stating in the notice the time and place where the election will be held and the purpose thereof; and the election may be held at any place in the city or town designated by the board whether the place be within or without the boundaries of the improvement district or districts. If no newspaper is published in the city or town, notice of the election shall be given by printed notices posted at ten (10) public places therein for more than twenty (20) days prior to the election.