The conjecture on infinitely many grids with discrepancy 2

Let $d_n$ denote the discrepancy associated with the grid of size $n$. The discrepancy-2 conjecture. There are infinitely many $n$ such that $d_n=2$. In particular, for all $k\in\mathbb{N}$, $d_{2\cdot 3^k-1}=2$. This parallels Sutner's result that there are infinitely many $n$ such that $d_n=0$; the statement is presented as unproved future work.