N.M. Stat. § 77-12-2
Whenever persons who own or hold under lease or contract of purchase a majority of the acres of contiguous tracts of land, aggregating not less than three thousand eight hundred and forty acres, shall file with the board of county commissioners of the county in which such lands or a major portion thereof, are situated, a petition in writing signed and acknowledged in the same manner as conveyances of deeds to real estate, and accurately defining such tracts of land and setting forth the correct acreage of each tract, requesting such board to declare such tracts of land a herd law district, said board of county commissioners shall, at the next regular or special meeting of said board, enter an order fixing the time and place, not less than twenty nor more than thirty days from the date of such regular or special meeting, for a hearing on said petition. The clerk of such board shall give notice of the time and place of such hearing by publishing a notice thereof in two successive issues of a legal newspaper of general circulation published nearest to the said proposed district. The last publication shall be not less than ten days prior to the date of said hearing. At the time and place fixed for said hearing said board of county commissioners shall hear said petition, and if it finds the same is duly signed and acknowledged as herein provided, by persons who are owners, lessees or contract purchase holders, of a majority of the acres of lands within said proposed districts and otherwise complies with the provisions of this act, it shall enter an order declaring that all of said tracts of land embraced in said proposed district, from and after thirty days from the date of said order, shall be a herd law district within the meaning of this act [77-12-1 to 77-12-12 NMSA 1978], and shall cause a notice thereof, accurately defining the boundaries of said district, and stating that said district from and after the expiration of thirty days from the date of said order shall be a herd law district within the meaning of this act, to be published in two consecutive issues of the same newspaper as the notice of said hearing. The last of such publications shall be not less than ten days prior to the date said order shall take effect. Provided, however, that no such herd law district shall be created unless at least one-fourth of the land embraced therein is being used for agricultural purposes.
NMS § 77-12-2