Planes of type B1 and B2 from projective geometries with dimension 4

BIBDs

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Planes of type B₁ and B₂ from projective geometries PG(4,q^ρν), ρ=2

The matrices showing the numbers of points per line, and vice versa, class by class are:

(B₁) Plane with one secant and (q^ν+1) points of the subgeometry.
		1	q^2ν(q^ν+1)	q^3ν(q^ν-1)
		s	t₂	x
q^ν+1	C₀	q^ν+1,1	1,q^2ν	0,0
q^2ν-q^ν	C₁₁	q^2ν-q^ν,1	0,0	1,q^2ν
q^4ν	C₁₂	0,0	q^2ν,q^ν+1	q^2ν,q^2ν-q^ν

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

(B₂) Plane with no secant and 1 point of the subgeometry.
		1	q^2ν	q^4ν
		t₁	t₂	x
1	C₀	1,1	1,q^2ν	0,0
q^2ν	C₁₁	q^2ν,1	0,0	1,q^2ν
q^4ν	C₁₂	0,0	q^2ν,1	q^2ν,q^2ν

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

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