Projective plane PG(2,23) of Type B3 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.

(B3) Plane with no secant or tangent and no point of the sub-geometry
  No 16 28 28 1
No Name x12 x11 x2 x3
8 C12 1,2 0,0 2,7 0,0
7 C11 0,0 1,4 1,4 7,1
56 C21 7,2 8,4 6,3 0,0
2 C22 1,8 0,0 0,0 2,1

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.

Note that this is the transpose of the plane of type B2 from the geometry PG(3,23) as described here.


Last Updated on 06/05/2004
By D.H.Rees