论文标题
球形包装的三分界限
Three-point bounds for sphere packing
论文作者
论文摘要
我们为球形填料定义了三点边界，以完善线性编程结合，并通过选择三点函数的截断半径来使用半决赛编程来计算这些边界。结果，我们在尺寸4到7和9至16中的球体堆积密度上获得了新的上限。我们还为晶格堆积和猜想提供了不同的三分界限，即该第二个界限在尺寸4中是锋利的。
We define three-point bounds for sphere packing that refine the linear programming bound, and we compute these bounds numerically using semidefinite programming by choosing a truncation radius for the three-point function. As a result, we obtain new upper bounds on the sphere packing density in dimension 4 through 7 and 9 through 16. We also give a different three-point bound for lattice packing and conjecture that this second bound is sharp in dimension 4.
