An upper bound on the smallest singular value of dense signed random combinatorial matrices

Let $M_n$ be an $n\times n$ random matrix with entries in $\{-1, 0, 1\}$, where each row is independently and uniformly sampled from the set of all vectors in $\{-1, 0, 1\}^n$ containing exactly $d$ nonzero entries, with $d=pn$ for some fixed constant $p\in(0,1/2]$. A recent result by one of the aut