区组长度为2^n-1因子的单纯3-设计

Simple 3-Designs with Block Size d Where d｜2^n- 1

令■=PSL(2,2n),X为射影直线,B为GF*(2n)=GF(2n)\{0}的阶为d的子群,其中d>5且当n/m为偶数时,d≠2m+1.通过确定(X,■(B))的参数集给出了一个单纯3-设计的无限族,并且证明了■(B)是惟一满足所构成的3-设计具有这种参数集的轨道.

Let y be PSL （2,2^n） , X be the projective line and B be any subgroup contained in GF^＊ （2^n） of order d, where d〉5 and d≠2^m＋1 when n/m is even. An infinite family of simple 3-designs was given by determining the parameter set of （X, Cy（B））. It was proved that y（B） is the unique orbit such that （X,y5（B）） is a simple 3-design with that parameter set.