N.M. Stat. § 77-16-4
When fences are constructed of barbed wire and posts they shall be built substantially as follows: posts set firmly in the ground aand [and] projecting above the ground not less than four feet, said posts to be not less than two inches in diameter at the smaller end, and to be set not over thirty-three feet apart; four barbed wires to be strung firmly and securely fastened to said posts, the bottom wire to be placed approximately twelve inches from the ground, the second wire to be approximately twelve inches above the bottom wire, the third wire to be approximately twelve inches above the second wire and the fourth wire to be approximately twelve inches above the third wire; and between each two posts there shall be placed approximately equidistant apart three stays to be securely fastened to said wires for the purpose of holding the wires in position. Any four-wire fence greater or equivalent to said fence in strength and resisting power shall be considered a legal fence.
NMS § 77-16-4