N.M. Stat. § 19-8-33
Nothing contained in this act [19-8-14 to 19-8-18, 19-8-21 to 19-8-33 NMSA 1978] shall be construed as requiring the commissioner to offer any tract or tracts of land for lease, but the commissioner shall have power to withhold any tract or tracts from leasing for said mineral purposes, if, in his opinion, the best interests of the state would be served by so doing, and nothing contained in this act shall be construed as prohibiting the commissioner from rejecting any application at any time prior to approval and offering acreage embraced therein for lease upon competitive bidding by sealed bids or at public auction to the bidder offering the highest bonus in addition to the annual rentals as set by the commissioner. Provided, however, that notice of such public sale shall be given by posting in a conspicuous place in the state land office, not less than ten (10) days before the date of sale, a notice of same, specifying the day and hour when, and the place where, the sale will be held, giving a description of the lands in each tract to be offered for lease. The notice shall also state whether the sale shall be conducted through sealed bids or at public auction and any other such information as the commissioner may deem necessary.
Where two or more sealed bids are received making the same offer on the same tract, the commissioner shall award the lease thereon in accordance with such regulations as he may prescribe.
NMS § 19-8-33