New Sphere Packings from the Antipode Construction

In this note, we construct non-lattice sphere packings in dimensions $19$, $20$, $21$, $23$, $44$, $45$, and $47$, demonstrating record densities that surpass all previously documented results in these dimensions. The construction involves applying the antipode method to suboptimal cross-sections of ${\mathrm{\Lambda }}_{24}$ and $P_{48p}$ respectively in those dimensions.