A new lower bound for Hermite's constant for symplectic lattices (Q2890256)

For symplectic lattices of dimension \(2g\) the paper gives a slight improvement of the lower bound on the density that was given in [\textit{P. Buser} and \textit{P. Sarnak}, Invent. Math. 117, No. 1, 27--56 (1994; Zbl 0814.14033)]. The author applies a similar (non constructive) proof as in the paper cited above to a subspace of symplectic lattices to show that the Hermite constant \(\delta _{2g} \geq \sqrt[g]{4g!}/\pi \). Related ideas have been used in [\textit{S. Vance}, ``Improved sphere packing lower bounds from Hurwitz lattices'', Adv. Math. 227, No. 5, 2144--2156 (2011; Zbl 1228.11095)].