Notice of the hearing shall be given by publication in the official county newspaper and in such other newspaper published in or near the district as the county legislative authority may in its discretion direct, once a week for two consecutive weeks, the last publication of which shall be not less than seven nor more than fourteen days before the date of the hearing. Also, the county legislative authority shall serve by mail, at least ten days before the hearing, upon the commissioner of public lands of the state two copies of the published notice of the hearing together with a statement showing the amount of benefits determined by the appraisers in respect of each parcel of state, school, granted, or other lands owned by the state in the district, and shall similarly serve notice of the hearing upon the secretary of transportation, with a statement showing the amount of benefits determined by the appraisers in respect of any state primary or secondary highways within the district.