  Building UV completions of lepton-number-violating effective operators has
proved to be a useful way of studying and classifying models of Majorana
neutrino mass. In this paper we describe and implement an algorithm that
systematises this model-building procedure. We use the algorithm to generate
computational representations of all of the tree-level completions of the
operators up to and including mass-dimension 11. Almost all of these correspond
to models of radiative neutrino mass. Our work includes operators involving
derivatives, updated estimates for the bounds on the new-physics scale
associated with each operator, an analysis of various features of the models,
and a look at some examples. We find that a number of operators do not admit
any completions not also generating lower-dimensional operators or larger
contributions to the neutrino mass, ruling them out as playing a dominant role
in the neutrino-mass generation. Additionally, we show that there are at most
five models containing three or fewer exotic multiplets that predict new
physics that must lie below 100 TeV. Accompanying this work we also make
available a searchable database containing all of our results and the code used
to find the completions. We emphasise that our methods extend beyond the study
of neutrino-mass models, and may be useful for generating completions of
high-dimensional operators in other effective field theories.
