Exponential quantum speedup for $\mathbb{F}_3^n$-Subset-Sum? Or, rigorous classical algorithms for Binary-Error LWE

We study vector subset sum over $\mathbb{F}_3^n$: given $m$ random vectors from $\mathbb{F}_3^n$, find a nonempty subset that sums to zero; the smaller $m$, the more difficult it is to find such a subset. Chen, Liu, and Zhandry (EUROCRYPT'22) introduced an efficient quantum algorithm that solves thi