N.M. Stat. § 14-11-10
Except as provided in the [Uniform] Probate Code [Chapter 45 NMSA 1978], all legal notices in connection with suits in the district courts, including notices of sale of property under any writ of execution, judgment, decree or other process issued out of the district court, and any notice of sale of personal property by virtue of any security interest, except as provided by the Uniform Commercial Code [Chapter 55 NMSA 1978], where the amount involved, including interest and costs, exceeds three hundred dollars ($300), shall be published in the English language in some newspaper of general circulation published in the county where such publication is required to be made, once each week for four consecutive weeks. If such publication shall be the notice of the pendency of a suit in the district court, the last insertion shall be at least twenty days before the date on or before which the defendant is notified to appear. In all other cases, the last insertion shall be at least three days before the date fixed in such notice for the taking of the action concerning which the publication is made. In case there be no newspaper published in the county where such publication is required, then publication shall be made by posting notice in at least six conspicuous places within the county for and during the period of time specified in the case of newspaper publications.
NMS § 14-11-10