  The discovery of high-$T_c$ conventional superconductivity in high-pressure
hydrides has helped establish computational methods as a formidable tool to
guide material discoveries in a field traditionally dominated by serendipitous
experimental search. This paves the way to an ever-increasing use of
data-driven approaches to the study and design of superconductors. In this
work, we propose a new method to generate meaningful datasets of
superconductors, based on element substitution into a small set of
representative structural templates, generated by crystal structure prediction
methods (MultiTemplate-HighThroughput approach). Our approach realizes an
optimal compromise between structural variety and computational efficiency, and
can be easily generalized to other elements and compositions. As a first
application, we apply it to binary hydrides at high pressure, realizing a
database of 880 hypothetical structures, characterized with a set of
electronic, vibrational and chemical descriptors. 139 structures of our
$Superhydra$ Database are superconducting according to the McMillan-Allen-Dynes
approximation. Studying the distribution of $T_c$ and other properties across
the database with advanced statistical and visualization techniques, we are
able to obtain comprehensive material maps of the phase space of binary
hydrides. The $Superhydra$ database can be thought as a first step of a
generalized effort to map conventional superconductivity.
