Projective plane PG(2,23) of Type B2 from a PG(3,23) of type D1

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.

(B2) Plane with no secant and 1 point of the sub-geometry
  No 3 6 16 48
No Name t1 t2 x y
1 C0 1,3 1,6 0,0 0,0
12 C1 4,1 0,0 3,4 1,4
12 C21 4,1 0,0 0,0 2,8
48 C22 0,0 8,1 6,2 6,6

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.

Note that this is the transpose of the plane of type B1 from the geometry PG(3,23) as described here.


Last Updated on 03/05/2004
By D.H.Rees