具有较小点数区本原对称设计的分类

THE CLASSIFICATION OF BLOCK-PRIMITIVE SYMMETRIC DESIGNS WITH SMALL POINTS NUMBER

研究区传递2-设计的分类是置换群与组合设计领域中的重要课题之一.目前关于区传递2-设计的分类主要集中在自同构群具有旗传递性和点本原性上.本文研究了区本原2-(v,k,λ)对称设计的分类问题,并证明了当设计的点数不大于200且自同构群不为仿射型时,在同构意义下只存在54个这样的设计.

The study of the classification of block-transitive 2-designs is one of the important topics in the field of permutation group and combinatorial designs.At persent,the classification of block-transitive 2-designs mainly focuses on the flag-transitivity and point-primitivity.In this article,we study the classification of block-primitive 2-(v,k,λ)symmetric designs,and prove the following result:Let D be a 2-(v,k,λ)symmetric design with v·200,and G be a block-primitive automorphism group of D.If G is not of a±ne type,then up to isomorphism there are only 54 such designs.