Iterated Topological Hochschild Homology of $\mathbb{F}_p$ at odd primes

We compute homotopy groups of $n$-fold iterated topological Hochschild homology of $\mathbb{F}_p$ for $n\geq1$ and odd primes. Identifying this as the Loday construction $T^n\otimes\mathbb{F}_p$, we construct a bar spectral sequence computing $π_*(T^n\otimes\mathbb{F}_p)$ and prove that this spectra