2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217204We give classifications of integral lattices which include the Barnes-Wall lattice $BW_{16}$ or laminated lattices of dimension $1 \leqslant d \leqslant 8$ and of minimum 4. Also, we give certain lattice neighboring from each lattice. Furthermore, we study spherical designs and the other properties.20 pages, 9 figures. http://www2.math.kyushu-u.ac.jp/~j.shigezumi/Combinatorics05B30; 03G10text