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Constructions for large sets of L-intersecting Steiner triple systems

机译:大型L相交的Steiner三重系统的构造

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Recently, Franek et al. introduced large sets of v - 1 L-intersecting Steiner triple systems of order v (STS(v)) and gave four constructions for them (Des., Codes and Cryptogr., 26 (2002), 243-256). In this paper, we mainly focus on large sets of v - 1 {0, 1}-intersecting STS(v) and large sets of v + 1{1}-intersecting STS(v). For this purpose, we introduce a concept of L-intersecting partitionable candelabra system (L-PCS) of order v with q(v) subsystems and establish a relationship between L-PCS and large set of q(v)L-intersecting STS(v). Some constructions for L-PCSs are also presented by 3-wise balanced designs. These facilitate the production of some new infinite classes of these large sets.
机译:最近,Franek等。引入了大的v-1级v-1 L相交的Steiner三元系统(STS(v)),并为其提供了四种构造(Des。,Codes and Cryptogr。,26(2002),243-256)。在本文中,我们主要关注与v-1 {0,1}相交的STS(v)的大集合和与v + 1 {1}相交的STS(v)的大集合。为此,我们引入了具有q(v)个子系统的v阶L相交可分割烛台系统(L-PCS)的概念,并建立了L-PCS与大量q(v)L相交STS( v)。 L-PCS的某些结构也通过3平衡设计来表示。这些有助于产生这些大型集合的一些新的无限类。

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