M_(12)作用在396个点上的SPBIB设计的分类

Classification of SPBIB Designs with v=396 and G=M_(12)

研究Mathieu群M_(12)作用在396个点上所构成的对称的部分平衡不完全区组设计(即SPBIB设计)的分类情况.首先,证明了以M_(12)作为自同构群的非平凡的2-(396,k,λ)对称设计是不存在的.然后,得到了同构意义下的3个点数为396且区组长度为80的SPBIB设计.最后,给出了396个点上以M_(12)作为自同构群的SPBIB设计的完全分类.

We focus on symmetric partially balanced incomplete block designs with automorphism group M12 acting on 396 points. To begin with, we proved that there is no non-trivial 2-（396, k, λ） symmetric design admitting M12 be an automorphism group. Then up to isomorphism, we obtained three SPBIB designs with v = 396 and k = 80. Finally, we gave the complete classification of SPBIB designs with v = 396 and automorphism group M12.