  We prove the Kakeya set conjecture for $\mathbb{Z}/N\mathbb{Z}$ for general
$N$ as stated by Hickman and Wright [HW18]. This entails extending and
combining the techniques of Arsovski [Ars21a] for $N=p^k$ and the author and
Dvir [DD21] for the case of square-free $N$. We also prove stronger lower
bounds for the size of $(m,\epsilon)$-Kakeya sets over
$\mathbb{Z}/p^k\mathbb{Z}$ by extending the techniques of [Ars21a] using
multiplicities as was done in [SS08, DKSS13]. In addition, we show our bounds
are almost sharp by providing a new construction for Kakeya sets over
$\mathbb{Z}/p^k\mathbb{Z}$ and $\mathbb{Z}/N\mathbb{Z}$.
