Upper Bound of Hermite Constant
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Theorem
Let $\gamma_n$ be the Hermite constant of dimension $n$.
Then:
- $\gamma_n \le \dfrac {\paren {1 + \epsilon_n} n} {\pi e}$
where $e_n \to 0$
Proof
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Sources
- 1929: H.F. Blichfeldt: The minimum value of quadratic forms, and the closest packing of spheres (Math. Ann. Vol. 101: pp. 605 – 608)
- 1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables ... (previous) ... (next): $1,33333 33333 33 \ldots$