Dense lattice packings of spheres in Euclidean spaces of dimension $n\leqslant16$

We present a number of lattice packings of equal spheres in $\mathbf R^n$ for $n\leqslant16$. For $n\leqslant15$, these packings have the same density as the densest known lattice packings. For $n=16$, the packing described here is denser than the known ones.