N.M. Stat. § 47-1-54
No coordinates based on the New Mexico coordinate system, purporting to define the position of a point on a land boundary, shall be presented to be recorded in any public land records or deed records unless such point is within eight kilometers of a monumented horizontal control station established by and for and for which coordinate data has been published by an agency of the state of New Mexico or a political subdivision of the state or established in conformity with the standards of accuracy and specifications for first-, second- or third- order geodetic surveying as prepared and published by the federal geodetic control committee of the United States department of commerce. Standards and specifications of the federal geodetic control committee or its successor in force on the date of the geodetic survey shall apply. The publication of the existing control stations, or the acceptance with intent to publish the newly established control stations by the national ocean survey and national geodetic survey, shall constitute evidence of adherence to the federal geodetic control committee's specifications. The limitations of this section may be further modified by the secretary of highway and transportation.
NMS § 47-1-54