Large sets of combinatorial designs has always been a fascinating topic in design theory. These designs form a partition of the whole space into combinatorial designs with the same parameters. In particular, a large set of block designs, whose blocks are of size k taken from an n-set, is a partition of all the k-subsets of the n-set into disjoint copies of block designs, defined on the n-set, and with the same parameters. The current most intriguing question in this direction is whether large sets of Steiner quadruple systems exist and to provide explicit constructions for those parameters for which they exist. In view of its difficulty no one ever presented an explicit construction even for one nontrivial order. Hence, we seek for related generalizations. As generalizations, to the existence question of large sets, we consider two related questions. The first one is to provide constructions for sets on Steiner systems in which each block (quadruple or a k-subset) is contained in exactly \(\mu \) systems. The constructions of such systems also yield secure protocols for the generalized Russian cards problem. The second question is to provide constructions for large set of H-designs (mainly for quadruples, but also for larger block size), which have applications in threshold schemes and in quantum jump codes. We prove the existence of such systems for many parameters using orthogonal arrays, perpendicular arrays, ordered designs, sets of permutations, and one-factorizations of the complete graph.

大型组合设计一直是设计理论中的一个引人入胜的话题。这些设计将整个空间划分为具有相同参数的组合设计。特别地，一大组块的设计，其块的大小的ķ从采取Ñ -set，是所有的分区ķ所述的-subsets Ñ -set成块的设计的不相交的副本，所定义的Ñ-set，并且具有相同的参数。这个方向上当前最引人入胜的问题是，是否存在大量的斯坦纳四元组系统，并为它们存在的那些参数提供显式构造。鉴于其困难，即使是对于一个非平凡的秩序，也没有人提出过明确的解释。因此，我们寻求相关的概括。作为概括，对于大集的存在问题，我们考虑两个相关的问题。第一个是为Steiner系统上的集合提供构造，其中每个块（四元组或k-子集）精确地包含在\（\ mu \）中系统。这种系统的结构还产生了针对普遍的俄罗斯卡问题的安全协议。第二个问题是为大型H设计（主要用于四倍，但也用于更大的块大小）提供构造，这些构造在阈值方案和量子跳跃码中都有应用。我们使用正交数组，垂直数组，有序设计，置换集和完整图的一次分解证明了针对许多参数的此类系统的存在。