With the SAMLAI, we exhaustively search the densest binary sphere packings (DBSP) under the periodic boundary condition with extending the unit cell compared to the previous study. Accordingly, we have updated the
phase diagram over the ($x$-$\alpha$) plane, where $x$ is the relative concentration and $\alpha$ is the radius ratio of the small sphere relative to the large sphere.

For $0.20 \le \alpha \le 0.40$, the exhaustive search is conducted for 11 radius ratios of $0.20$, $0.22$, $0.24$, $0.26$, $0.28$, $0.30$, $0.32$, $0.34$, $0.36$, $0.38$, and $0.40$. In order to confirm
that the (12-1) structure appears on the phase diagram, the XY_{12} structure, the XY_{11} structure, and the (22-1) structure are re-optimized at $\alpha = 0.203$. The number of spheres in the unit cell is set between
6 and 24. As a result, we have identified the new six putative DBSP: the XY_{12} structure, the (22-1) structure, the (12-1) structure, the (20-1) structure, the (8-2) structure, and the (2-1) structure.

For $0.420 \le \alpha \le 0.500$, the exhaustive search is conducted for 17 radius ratios of $0.420$, $0.425$, $0.430$, $0.435$, $0.440$, $0.445$, $0.450$, $0.455$, $0.460$, $0.465$, $0.470$, $0.475$, $0.480$,
$0.485$, $0.490$, $0.495$, and $0.500$. In order to confirm that the (9-4) structure appears on the phase diagram, the (2-2) structure, the (10-4) structure, the AuTe_{2} structure and the (9-4) structure are re-optimized at
$\alpha = 0.481$, $0.482$, and $0.483$. The number of spheres in the unit cell is set between 12 and 32. As a result, we have identified 5 new putative DBSP: the (14-5) structure, the (16-4) structure, the (8-4) structure, the (10-4)
structure, and the (9-4) structure. The details are discussed in the latest paper.

For $0.52 \le \alpha \le 0.64$, the exhaustive search is conducted for 7 radius ratios of $0.52$, $0.54$, $0.56$, $0.58$, $0.60$, $0.62$, and $0.64$. The number of spheres in the unit cell is set between
6 and 24. As a result, we have identified one new putative densest packing: the (12-6) structure.

The XY_{n} structure is defined as DBSP in which large spheres X constitute the fcc densest structure and small spheres penetrate into the tetrahedral and octahedral sites constituted by X. If the
XY
_{n} are excluded, there are 21 putative DBSP on the phase diagram. Most of those structures are named as ($m$-$n$) structure. A ($m$-$n$) structure contains $m$ small spheres and $n$ large spheres.

The phase diagram

When the highest packing fraction is achieved by phase separation into densest binary packing R and the fcc densest packing constituting of small spheres, only the symbol of the densest binary packing R is plotted.
On the other hands, when the highest packing fraction is achieved by phase separation into two densest binary packings, those two symbols are plotted together.

The three-dimensional data of the DBSP for the phase diagram are downloadable