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.
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机译：我们找出自对偶格子及其阴影的$ t $壳是球形的$ t $-设计。该方法使用θ系列的格子，它们是模块化形式。我们分析的是完全立方和维特格子，以及所有等级最多为24的自对偶格子。
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