  Recently an algorithm to build $SL(2,\mathbb{Z})$ duals, including mirror
duals, of 3d $\mathcal{N}=4$ quiver theories and their 4d $\mathcal{N}=1$
uplift has been introduced. In this work we use this new tool to study the
so-called bad theories. Our approach allows us to determine exactly
indices/partition functions for generic values of fugacities/real mass and FI
parameters revealing their surprising feature: the 4d index/3d partition
function of a bad theory behaves as a sum of distributions rather than an
ordinary function of the deformation parameters. We focus on the bad SQCD, with
$U(N_c)$ gauge group in 3d and $USp(2N_c)$ in 4d, while in an upcoming paper we
will consider linear quivers which, in the 3d case, have both unitary and
special unitary bad nodes.
