Neb. Rev. Stat. §§ 16-672.05
After ordering improvements as provided in section 16-672.01, the mayor and city council may enter into a contract for the construction of the improvements in one or more contracts, but no work shall be done or contract let, if the estimated cost of the improvements, as determined by the city engineer, is in excess of two thousand dollars, until notice to contractors has been published once each week for three weeks in a legal newspaper in or of general circulation in the city. The notice shall state the extent of the work, and the kind of materials to be bid upon, including in such notice all kinds of material mentioned in the ordinance specified in section 16-672.01, and the time when bids will be received, and may set forth the amount of the engineer's estimate of the cost of such improvements. The work provided for in sections 16-672.01 to 16-672.11 shall be done under a written contract with the lowest responsible bidder on the material selected after the bids are opened and in accordance with the requirements of the plans and specifications. The mayor and city council may reject any or all bids received and advertise for new bids in accordance with this section.
Neb. Rev. Stat. §§ 16-672.05