  We present the largest full N-body simulation to date with local primordial
non-Gaussianities (L-PNG), the \textsc{PNG-UNITsim}. It tracks the evolution of
$4096^3$ particles within a periodic box with $L_{\rm box} = 1 \; h^{-1}\,{\rm
Gpc}$, leading to a mass resolution of $m_{p} = 1.24\times 10^{9}\;
h^{-1}\,M_\odot$. This is enough to resolve galaxies targeted by stage-IV
spectroscopic surveys. The \textsc{PNG-UNIT} has \textit{Fixed} initial
conditions whose phases are also \textit{Matched} to the pre-existing
\textsc{UNIT} simulation. These two features in the simulations reduce our
uncertainty significantly so we use 100 \textsc{FastPM} mocks to estimate this
reduction. The amplitude of the non-Gaussianities used to set the initial
conditions of this new simulation is $f_{\rm NL}^{\rm local} = 100$. In this
first study, we use mass selected dark matter haloes from the \textsc{PNG-UNIT}
simulation to constrain the local PNG parameters. PNG induce a scale dependent
bias, parameterised through \bp or $p$, which might depend on the type of
cosmological tracer. Those cases when $p=1$ are referred to as the {\it
universality relation}. We measure $p$ as a function of the halo mass. Haloes
with masses between $1\times 10^{12}$ and $2\times 10^{13} \, h^{-1} M_\odot$
are well described by the {\it universality relation}. For haloes with masses
between $2\times 10^{10}$ and $1\times 10^{12} \, h^{-1} M_\odot$ we find that
$p<1$ at $3\sigma$. Combining all the mass bins, we find $p$ consistent with a
value of $0.955\pm0.013$, which is $3\sigma$ away from \textit{universality},
as low mass haloes are more numerous. We also study the effect of using priors
on $p$ when constraining $f_{\rm NL}$. Using the values we obtain for $b_\phi$
as priors, we forecast that a DESI-like (stage-IV) survey will be able to
constrain $f_{\rm NL}$ better than if the universality relation is assumed.
