The numbers of lines (points) of the various types are given in the first row (column) of the table following. The notation follows that given for the 3-dimensional geometry: some of the types are further sub-divided here, so that only the first suffices are significant.
| No | 1 | 12 | 36 | 24 | 192 | 8 | |
|---|---|---|---|---|---|---|---|
| No | Name | s | t1 | t2 | x1 | x2 | x4 |
| 3 | C0 | 3,1 | 1,4 | 1,12 | 0,0 | 0,0 | 0,0 |
| 12 | C111 | 12,1 | 0,0 | 0,0 | 0,0 | 1,16 | 0,0 |
| 2 | C1121 | 2,1 | 0,0 | 0,0 | 1,12 | 0,0 | 1,4 |
| 16 | C1122 | 0,0 | 4,3 | 0,0 | 0,0 | 1,12 | 4,2 |
| 144 | C21 | 0,0 | 12,1 | 8,2 | 12,2 | 9,12 | 0,0 |
| 96 | C22 | 0,0 | 0,0 | 8,3 | 4.1 | 6,12 | 12,1 |
The complete design above is a BIBD with λ=1.
As the symmetry between points and lines is lost in the detailed breakdown, different subdesigns are available according to whether points or lines are taken as treatments.
Last Updated on 22/02/2004
By D.H.Rees