  The motivation for this paper comes from the ongoing SARS-CoV-2 Pandemic. Its
goal is to present a previously neglected approach to non-adaptive group
testing and describes it in terms of residuated pairs on partially ordered
sets. Our investigation has the advantage, as it naturally yields an efficient
decision scheme (decoder) for any given testing scheme. This decoder allows to
detect a large amount of infection patterns. Apart from this, we devise a
construction of good group testing schemes that are based on incidence matrices
of finite partial linear spaces. The key idea is to exploit the structure of
these matrices and make them available as test matrices for group testing.
These matrices may generally be tailored for different estimated disease
prevalence levels. As an example, we discuss the group testing schemes based on
generalized quadrangles. In the context at hand, we state our results only for
the error-free case so far. An extension to a noisy scenario is desirable and
will be treated in a subsequent account on the topic.
