A PG(3,2) gives a BIBD(15,35,7,3,1). Using homogeneous coordinates x and y to denote the points, a plane is represented by the equation α'x=0. The correlation may be defined by x'Py=0: to the point x corresponds the set of points y such that (x'P)y = 0 (and vice versa). Here, the matrix adopted is:

0	1	0	0
1	0	0	0
0	0	0	1
0	0	1	0

and this gives the following correspondence between points and planes, where lower case letters a,b, etc denote the points of the planes, having the same coordinates as the upper case letters. (For example, a = (0001), d = (0100), both satisfy the equation (0 0 1 0)x = 0 involving the point A which is also (0001), and the matrix P above, and so both belong to the plane α corresponding to A.)

Point	Coords	Plane
A	(0001)	a,d,e,h,i,l,m
B	(0010)	b,d,f,h,j,l,n
C	(0011)	c,d,g,h,k,l,o
D	(0100)	a,b,c,d,e,f,g
E	(0101)	a,d,e,j,k,n,o
F	(0110)	b,d,f,i,k,m,o
G	(0111)	c,d,g,i,j,m,n
H	(1000)	a,b,c,h,i,j,k
I	(1001)	a,f,g,h,i,n,o
J	(1010)	b,e,g,h,j,m,o
K	(1011)	c,e,f,h,k,m,n
L	(1100)	a,b,c,l,m,n,o
M	(1101)	a,f,g,j,k,l,m
N	(1110)	b,e,g,i,k,l,n
O	(1111)	c,e,f,i,j,l,o

By constructing the lines of the geometry from the points, and the corresponding lines from the intersections of the corresponding planes, the following partial design is obtained (in resolved form):

BHJ,bhj	ALM,alm	FIO,fio	EKN,ekn	CDG,cdg
AHI,ahi	FKM,fkm	CLO,clo	BEG,djn	DJN,beg
CKH,ckh	ADE,ade	GIN,gin	BMO,fjl	FJL,bmo
BLN,bln	GHO,cij	AJK,ehm	CEF,dko	DIM,afg
BDF,bdf	EHM,ajk	CIJ,gho	GKL,cmn	ANO,eil
GJM,gjm	FHN,bik	ABC,dhl	DKO,cef	EIL,ano
EJO,ejo	DHL,abc	BIK,fhn	CMN,gkl	AFG,dim

All that remains is to match the points within the lines: in the original paper this was done by trial-and-error, but some improvement to that can be made.