LD设计的存在谱

Existence Spectrum of LD Designs

在解决斯坦纳三元系大集存在性问题时,陆家羲引入LD设计和LD^(*)设计的概念,建立这两类设计的若干递推构造和直接构造,在构作斯坦纳三元系大集过程中发挥重要作用.为了构造陆家羲遗留的六个小阶数的斯坦纳三元系大集,Teirlinck依然借助LD设计,使用PBD进行递推构造,最终确定斯坦纳三元系大集的存在谱.本文将彻底解决LD设计存在的充分必要条件,对LD^(*)设计的存在性仅余四个可能例外值.

The Chinese mathematician Jiaxi Lu introduced the concepts of LD design and LD^(*) design in the process of resolving the existence problem of large sets of Steiner triple systems(LSTSs).Lu also presented several recursive constructions and direct constructions for the two types of designs,which played vital roles in producing LSTSs.In order to deal with the remaining six possible exceptions for the existence of LSTSs,Teirlinck still employed LD designs in the recursive constructions using pairwise balanced designs and then he resolved the problem of LSTSs completely.This paper proves that the necessary conditions are all sufficient for the existence of LD designs and there leaves only four possible exceptions for LD^(*) designs.