N.M. Stat. § 19-4-16
Such lots or parcels of land shall be sold at public vendue to the highest bidder for cash and shall be offered for sale singly unless a greater price can be obtained by selling several lots or parcels of land together, in which case several lots or parcels of land can be sold together, after an attempt has been first made to sell them singly. Such sale may be continued if necessary, from day to day for a period not to exceed three days at any one sale. In case all said lands are not sold at first sale, the remaining lands shall be advertised as many times as may be necessary to sell said lands, and all sales subsequent to the first sale shall be advertised and conducted the same as the first sale. No lot or parcel of land shall be sold at less than its appraised value. A new appraisement may be had of all lands remaining unsold: provided, that such new appraisement shall not be made oftener than three months. Such new appraisement shall be made by a new board of appraisers, or the old board of appraisers, to be appointed in the manner of the first board of appraisers.
NMS § 19-4-16