A second projective plane PG(2,24) of Type B1.

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.

(B1) Plane with one secant and 3 points of the sub-geometry
  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