The Hermite constant is defined for dimension n as the value γ_n = (sup_f min_x_i f(x_1, x_2, ..., x_n))/[discriminant(f)]^(1/n) (Le Lionnais 1983). In other words, they are given by γ_n = 4(δ_n/V_n)^(2/n), where δ_n is the maximum lattice packing density for hypersphere packing and V_n is the content of the n-hypersphere. The first few values of (γ_n)^n are 1, 4/3, 2, 4, 8, 64/3, 64, 256, ... (OEIS A007361 and A007362, p. 518). Values for larger n are not known.

discriminant | hypersphere packing | kissing number | sphere packing