2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74208We find out for which $t$ shells of selfdual lattices and of theirs shadows are spherical $t$-designs. The method uses theta series of lattices, which are modular forms. We analyse fully cubic and Witt lattices, as well as all selfdual lattices of rank at most 24.Combinatoricstext