A construction of designs on n+1 points from multiply homogeneous permutation groups of degree n

作者：Miyamoto Izumi^*

来源：Journal of Combinatorial Theory - Series A, 2010, 117(4): 430-439.

DOI：10.1016/j.jcta.2009.07.011

• t-Design
• Homogeneous permutation group
• Projective special linear group

A simple criterion to construct a t-design on n + 1 points from a t-ply homogeneous permutation group of degree n using some orbits of the group is obtained. The design is not simple in general. Applying the criterion to 2-dimensional projective special linear groups PSL(2,q) for q >= 19 acting on the projective line of q points, simple 3-(q + 2, 1/2(q - 1), 1/24(q - 1)(q - 3)(q - 5)) designs are obtained if q 3 or 7 (mod 12), and simple 3-(q + 2, 1/2 (q + 1), 1/8 (q - 1)(2)(q - 3)) designs are obtained if q 3 (mod 4).

• 出版日期2010-5