Simple 3‐Designs of PSL(2,2n) With Block Size 13

ABSTRACT This paper focuses on the investigation of simple 3‐ designs admitting as an automorphism group. Such designs arise from the orbits of 13‐element subsets under the action of on the projective line , and any union of these orbits also forms a 3‐design. Therefore, the possible values of only depend on the number of orbits with each stabilizer size. We determine the total number of orbits when acts on 13‐element subsets of and classify all realizable values of .