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
(a) the 35 partitions of an 8-set H (such as GF(8) above, or Conwell's 8 "heptads") into two 4-sets, and
(b) the 35 partitions of L into four parallel affine planes.
Two of the H-partitions have a common refinement into 2-sets iff the same is true of the corresponding L-partitions. (Cameron , p. 60).
Note that C is particularly natural in row 1, and that partitions 2-5 in each row have similar structures.
For an image of the original 1985 typed note, click here.