Finite Geometry Notes

Steven H. Cullinane
Generating the Octad Generator
Expository note. April
28, 1985.
Apart from its use in studying the 759 octads of a
Steiner system
(a) the 35 partitions of an 8set H (such as GF(8) above, or
Conwell's 8 "heptads") into two 4sets, and
(b) the 35 partitions of L into four parallel affine planes.
Two of the Hpartitions have a common refinement into 2sets iff the same is true of the corresponding Lpartitions. (Cameron [1], p. 60).
Note that C is particularly natural in row 1, and that partitions 25 in each row have similar structures.
For an image of the original 1985 typed note, click here.