Reachability in 3-VASS is in Tower

The reachability problem for vector addition systems with states (VASS) has been shown to be $\text{textsc}Ackermann$-complete. For every $k\ge 3$, a completeness result for the $k$-dimensional VASS reachability problem is not yet available. It is shown in this paper that the $3$-dimensional VASS reachability problem is in $\text{textsc}Tower$, improving upon the current best upper bound ${\mathbf{F}}_7$ established by Leroux and Schmidt in 2019.