  Since spin currents can be generated, detected, and manipulated via the spin
Hall effect (SHE), the design of strong SHE materials has become a focus in the
field of spintronics. Because of the recent experimental progress also the spin
Nernst effect (SNE), the thermoelectrical counterpart of the SHE, has attracted
much interest. Empirically strong SHEs and SNEs are associated with $d$-band
compounds, such as transition metals and their alloys -- the largest spin Hall
conductivity (SHC) in a $p$-band material is $\sim 450$
$\left(\hbar/e\right)\left(\Omega\cdot cm\right)^{-1}$ for a Bi-Sb alloy, which
is only about a fifth of platinum. This raises the question whether either the
SHE and SNE are naturally suppressed in $p$-bands compounds, or favourable
$p$-band systems were just not identified yet. Here we consider the $p$-band
semimetal InBi, and predict it has a record SHC $\sigma_{xy}^{z}\approx 1100 \
\left(\hbar/e\right)\left(\Omega\cdot cm\right)^{-1}$ which is due to the
presence of nodal-lines in its band structure. Also the spin-Nernst
conductivity $\alpha_{zx}^y\approx 1.2 \ (\hbar/e)(A/m\cdot K)$ is very large,
but our analysis shows its origin is different as the maximum appears in a
different tensor element. This insight gained on InBi provides guiding
principles to obtain a strong SHE and SNE in $p$-band materials and establishes
a more comprehensive understanding of the relationship between the SHE and SNE.
