PSL(2,2ⁿ)与单纯3-(2ⁿ + 1,2ld + 1,λ)设计(l为奇数,d|(2ⁿ - 1)且d ≥ 3)

PSL(2,2ⁿ) and Simple 3-(2ⁿ + 1,2ld + 1,λ) Designs Where l Is Odd, d|(2ⁿ - 1) and d ≥ 3

令X=GF(q)∪{∞}是射影直线。设l为奇数,d为满足d丨(2n-1)且d ≥ 3的正整数。本文确定了以PSL(2,2n)为自同构群,区组长度为2ld + 1,初始区组的稳定子群中含有d阶元的单纯3-设计的参数,并计算了构成这一参数的轨道的条数。利用PSL(2,2n)在X上作用的轨道,得到如下结论:这类单纯3-设计的参数为3-(2n + 1,2ld + 1,2l(2ld-1)(2ld+1)),构成这一设计的轨道的条数为。

Let X=GF(q)∪{∞} be the projective line.Let l be an odd integer.The integer d satisfies d丨(2n-1)and d≥3.In this paper,we determined the parameter set of simple 3-designs from PSL(2,2n)with block size 2ld+1 where the stabilizer of the initial block contains order d element of PSL(2,2n)and calculated the number of the orbits which form the simple 3-design with that pa-rameter set.By using the orbits of PSL(2,2n)on the X,the results show that the number of the orbits is which forms the simple 3-(2n+1,2ld+1,2l(2ld-1)(2ld+1))design.