An exclusive set system is a family of subsets of a universe with the property that every large subset may be written as the union of subsets from the family. We obtain new upper bounds on the size of such families, showing that in a universe of n elements, there is a system of 48k3 (nk)r/k In subsets with the property that every subset of the universe of size n -- r can be written as the union of k subsets in the system. Such sets systems form the combinatorial foundation of many broadcast encryption schemes.
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机译：排他集系统是Universe的子集族，其属性是每个大子集都可以写为该族子集的并集。我们获得了此类族的大小的新上限，表明在n个元素的宇宙中，存在着一个由48 k 3 （ nk ） r / k 在具有以下性质的子集中，宇宙的每个子集的大小为 n - r 可以写为系统中 k 个子集的并集。这样的集合系统形成许多广播加密方案的组合基础。
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