R. Scharlau, B. Venkov, The genus of the Barnes-Wall lattice, Comment. Math. Helvetici 69 (1994), 322-333 Home/Search Document Details and Download
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The Shadow Theory of Modular and Unimodular Lattices - Rains, Sloane (3 citations) (Correct)
....examples of modular lattices meeting the bounds of Theorems 1 and 2 (and of the analogous bounds in Section 7) can be found for instance in [2] 15] 28] 31] 32] 34] 37] 38] 39] Other examples will be constructed here. Some nonexistence results are given in [35] and [43] see also [44], 45] For unimodular lattices, the highest possible minimal norm is known for dimensions n 33 and 40 48 [13] 17] and in this range the bound of Theorem 1 is achieved precisely for n = 8; 12; 14 Gamma 24; 32 and 40 48. For N = 2, lattices achieving the bound of Theorem 2 are known (see ....
R. Scharlau and B. B. Venkov, The genus of the Barnes-Wall lattice, Comm. Math. Helv. 69 (1994), 322--333.
Modular Forms, Lattices and Spherical Designs - Bachoc, Venkov (2000) Self-citation (Venkov) (Correct)
.... L = L 0 by setting 2( 1) to be the smallest of the minimum of L and L 0 , and by fixing the two series L and L 0 . 6 20 dimensional level 2 lattices of determinant 2 10 The genus of the level 2 lattices of dimension n and determinant 2 n=2 is classified up to dimension n = 16 [S V1]. In dimension 16, there are 24 classes, among which only one has minimum 4, which is the one of the Barnes Wall lattice (this last characterisation of the Barnes Wall lattice was shown in [Que95] In dimension 20, there is no complete classification, but three lattices of minimum 4 are known. ....
R. Scharlau, B. Venkov, The genus of the Barnes-Wall lattice, Comment. Math. Helvetici 69 (1994), 322-333
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