Lines of the 3-space of type D1 of the projective geometry PG(4,23) with sub-geometry

This 3-space has 7 points of the sub-geometry, whereas the "normal" subspace would have 15.

PG(3,23) of type D1
    7 42 112 336 1344 1536 1344 24
    sec t1 t21 t22 x11 x12 x2 x3
7 C0 3,3 1,6 1,16 1,48 0,0 0,0 0,0 0,0
42 C11 6,1 4,4 0,0 0,0 1,32 0,0 1,32 7,4
64 C12 0,0 0,0 4,7 0,0 0,0 1,24 2,42 0,0
448 C21 0,0 0,0 4,1 8,6 8,24 7,24 6,18 0,0
24 C22 0,0 4,7 0,0 0,0 0,0 1,64 0,0 2,2

The complete design above is a BIBD with λ=1.

I have given three previously undefined planes to be found in this 3-space: the remaining planes in it are the "normal" one of type B0 and the plane of type B1 given here.


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