Strichartz estimate for discrete Schrödinger equation on layered King's grid

We establish the sharp $l^1\to l^{\mathrm{\infty }}$ decay estimate for the discrete Schrödinger equation (DS) on the Layered King’s Grid (LKG), with a dispersive decay rate of $⟨t{⟩}^{-13\mathrm{/}12}$, which is faster than that for $3$-dimensional lattice ($⟨t{⟩}^{-1}$, see \cite{SK05}). This decay estimate enables us to derive the corresponding Strichartz estimate via the standard Keel–Tao argument. Our approach relies on using techniques from Newton polyhedra to analyze singularities.