  The Nelson-Seiberg theorem and its extensions relate supersymmetry breaking
and R-symmetries in Wess-Zumino models. But their applicability may be limited
by previously found non-generic counterexamples. Constructing a dataset of
R-symmetric Wess-Zumino models is useful for studying the occurrence of such
counterexamples as well as other purposes. This work gives a pedagogical review
on the basics of supersymmetry in (3+1)-dimensions, Wess-Zumino models and
their supergravity extensions, the Nelson-Seiberg theorem and its extensions.
We present a preliminary construction of the dataset of R-symmetric Wess-Zumino
models with up to 5 chiral fields. Among 925 models in total, 20 of them with
non-generic R-charges are counterexamples to both the Nelson-Seiberg theorem
and its extensions. Thus the dataset gives an estimation of the accuracy of the
field counting method based on these theorems. More constructions and
applications of the dataset are expected in future work.
