## Packings

We develop the software package to explore the densest sphere packings. To efficiently explore the densest structures, we develop an unbiased random search approach based on both a piling up method to generate initial structures in an unbiased way and an iterative balance method to optimize the volume of unit cell while keeping the overlap of hard spheres minimized. The details of our methods are discussed in the latest paper. The distribution of the program package and the source codes follow the practice of the GNU General Public License version 3 (GPLv3), and they are downloadable from this Website.
In the latest research, we revisit the densest binary sphere packings under periodic boundary conditions and present an updated phase diagram, including newly found 12 putative densest structures over the $x-\alpha$ plane, where $x$ is the relative concentration and $\alpha$ is the radius ratio of the small and large spheres. The phase diagram is shown here and the three-dimensional data of the densest binary sphere packings are also downloadable there.