The $RO(\mathcal{K})$-graded homotopy of Klein-four normed Mackey functors

We compute the $RO(\mathcal{K})$-graded coefficients of the equivariant Eilenberg-Mac Lane spectrum associated to various Hill-Hopkins-Ravenel norms of the constant-$\mathbb{F}_2$ Mackey functor, where $\mathcal{K}$ is the Klein-four group. Further, we analyze the multiplicative structure of these $RO(\mathcal{K})$-graded Tambara functors.