  This paper presents the results of an extensive structural search of ternary
solids containing lutetium, nitrogen and hydrogen. Based on thousands of
thermodynamically stable structures, available online, the convex hull of the
formation enthalpies is constructed. To obtain the correct energetic ordering,
the highly accurate RSCAN DFT functional is used in high quality all-electron
calculations. In this way possible pseudopotential errors are eliminated. A
novel lutetium hydride structure (HLu$_2$) that is on the convex hull is found
in our search. An electron phonon analysis however shows that it is not a
candidate structure for near ambient superconductivity. Besides this structure,
which appears to have been missed in previous searches, possibly due to
different DFT methodologies, our results agree closely with the results of
previously published structure search efforts. This shows, that the field of
crystal structure prediction has matured to a state where independent
methodologies produce consistent and reproducible results, underlining the
trustworthiness of modern crystal structure predictions. Hence it is quite
unlikely that a structure, that would give rise within standard BCS theory to
the superconducting properties, claimed to have been observed by
Dasenbrock-Gammon et al. 10.1038/s41586-023-05742-0 , exists. This solidifies
the evidence that no structure with conventional superconducting properties
exists that could explain the experimental observation made by
Dasenbrock-Gammon et al. 10.1038/s41586-023-05742-0
