可分组t-设计及相关设计

可分组t-设计是t-设计的推广，可分组2-设计在“Wilson 基本构作法”中充当主导设计的角色，可分组3-设计在Hartman的3-平衡设计基本构作中起重要作用，确定可分组t-设计的存在性是当代组合设计中最基本的经典核心问题之一。当t≥3时, 由于难度很大，所以已知结果有限，有许多重要问题有待于研究解决。本项目拟研究可分组t-设计、3平衡设计闭集最小生成集、自同构群为交换群且对称的正则斯坦纳四元系、旋转斯坦四元系、具有几乎生成区组设计的斯坦纳四元系、可用于常重复合码的特殊三元系超大集与有向的可分组3-设计的构作方法和存在性。这些问题都是近些年国内外组合设计界关注的热点问题，对它们的研究有助于推动组合设计理论与应用的发展。

The group divisible t-design is a generalization of the t-design. Group divisible 2-designs act as master designs in "Wilson's Fundamental Construction", while group divisible 3-designs play an important role in Hartman's fundamental construction for 3-wise balanced designs. The determination of the existence of such designs is a basic problem in design theory. For t≥3, not much is known because it is hard to construct them. Based on our previous work, we shall study the existence of group divisible t-designs, the minimal generating sets of three wise balanced design closed sets, Steiner quadruple systems with a point-regular automorphism group, with an alomost spanning block design, special overlarge sets of Steiner triple systems and ordered group divisible 3-designs for constant-composition codes recently. Such research problems have been received much attention. The progress of our research can promote the development of combinatorial designs.