An integral lattice which is generated by some vectors of norm q is called q-lattice. Classification of 3-lattices of dimension at most four is given by Mimura (On 3-lattice, 2006). As a expansion, we give a classification of 3-lattices of dimension at most seven. In addition, we consider the spherical designs from its shells. We use `Magma' for the classification.
References
References
[1] Y. Mimura, On 3-lattices (Japanese), The journal of Kobe Pharmaceutical University in humanities and mathematics, 7 (2006), 29-42.
[2] J. Shigezumi, On 3-lattices and spherical designs, preprint. [arXiv:0810.4373[math.CO]]
The following datas include lists of Gram matrices of irriducible 3-lattices of each dimension: