  We survey the landscape of binary hydrides across the entire periodic table
from 10 to 500 GPa using a crystal structure prediction method. Building a
critical temperature ($T_c$) model, with inputs arising from density of states
calculations and Gaspari-Gyorffy theory, allows us to predict which
energetically competitive candidates are most promising for high-$T_c$
superconductivity. Implementing optimisations, which lead to an order of
magnitude speed-up for electron-phonon calculations, then allows us to perform
an unprecedented number of "high-throughput" calculations of $T_c$ based on
these predictions and to refine the model in an iterative manner. Converged
electron-phonon calculations are performed for 121 of the best candidates from
the final model. From these, we identify 36 above-100 K dynamically stable
superconductors. To the best of our knowledge, superconductivity has not been
previously studied in 27 of these. Of the 36, 18 exhibit superconductivity
above 200 K, including structures of NaH$_6$ (248-279 K) and CaH$_6$ (216-253
K) at the relatively low pressure of 100 GPa.
