The conservative Washington Examiner reported Thursday that no GOP candidate will appear on the ballot for the U.S. Senate race because they failed to meet all requirements.

Of the three republicans who ran, NONE qualified to appear on the ballot for the New Mexico senate.

The Albuquerque Journal reported it is the first time in modern history that a Republican won't even appear on the ballot

and for a candidate to qualify:

Candidates must submit a nominating petition signed by a number of voters equal to at least two percent (2%) of the total vote of the candidate’s party in the state or congressional district

...and for context:

Lujan won his first Senate election in 2020 with 51.72% of the vote, compared to his Republican rival’s 45.62%.