Designs with block-size 6 in projective planes of characteristic 2
The paper under review lists the action of the projective group and the number of orbits on every possible set of six points in \(PG(2,q)\), \(q\) even. A similar result on 4-, 5- and 6-sets of the projective line is presented. From this, one constructs a number of 3 and 4 designs with block size 6 admitting \(PGL_ 3(q)\) as an automorphism group (transitive on the points, never transitive on the blocks). These constructions generalize dramatically the construction of 4-designs due to \textit{W. O. Alltop} [J. Comb. Theory 6, 320-322 (1969; Zbl 0169.019)].
scientific article; zbMATH DE number 93437