%0 Journal Article %T Shells of selfdual lattices viewed as spherical designs %A Claude Pache %J Mathematics %D 2005 %I arXiv %X We 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. %U http://arxiv.org/abs/math/0502313v1