2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/172377An 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.199 pages, http://www2.math.kyushu-u.ac.jp/~j.shigezumi/L3/Combinatorics05B30; 03G10text