完美的强共规格是周期极值
Perfect, strongly eutactic lattices are periodic extreme
摘要：
我们引入了一个参数空间的周期点集，给出了作为工会的$m$翻译的点格。在这篇文章中，我们研究了球填充密度函数的行为，并得到了局部最优性的充分条件。使用这些标准，我们证明了完美的，强共规格不能局部改进，以产生更大的密度周期性球包装。这特别适用于在维度$d\leq 8$和$d=24$中的已知的晶格球填充。
英文摘要：
We introduce a parameter space for periodic point sets, given as unions of $m$ translates of point lattices. In it we investigate the behavior of the sphere packing density function and derive sufficient conditions for local optimality. Using these criteria we prove that perfect, strongly eutactic lattices cannot be locally improved to yield a periodic sphere packing with greater density. This applies in particular to the densest known lattice sphere packings in dimension $d\leq 8$ and $d=24$.
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