What is the best known lattice for sphere packing in dimension 9? The 'best' lattice is still unknown in dimension $d>8$ (except for the famous d=24!)
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http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/density.html – Will Jagy Jul 06 '18 at 18:38
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I see. Table 1.2 in the first chapter of SPLAG does also mention a $P_{9a}$ non-lattice packing. It has a higher (maximum) kissing number than $\Lambda_9$ but not as good density. So Nebe's table does not mention it, although non-lattice packings are mentioned for dimensions 10,11,13,.. – Will Jagy Jul 06 '18 at 18:41
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similar on page 3 of Sloane: https://arxiv.org/pdf/math/0207256.pdf note that Sloane and Nebe are joint administrators of the lattice index... – Will Jagy Jul 06 '18 at 19:11