The qanalog of the KramerMesner matrix 
The next step in the construction is the evaluation of the entries of the KramerMesner matrices. We achieve this goal by using the information obtained during the ladder game.
We can restrict attention to KramerMesner matrices , because of
(The analogous equation  with binomial coefficients instead of the Gaussian numbers  holds for designs on sets, the proof of it is easily generalized to the analog.
The matrix can be obtained as follows: We assume the representatives of the double cosets of and , representatives of the double cosets of and and the corresponding orbit graph. Now the entry of indexed by the orbits
is
where the sum is over all double cosets which are connected with the double coset and which are connected with the double coset at the same time.
If we take our last example then we get the KramerMesner matrix:
(3,0,4) 
(3,1,2,) 
(3,2,6) 
(3,3,6) 
(3,4,8) 
(3,5,4) 

(5,0,6) 
6/2 
6/2 
0 
6/6 
0 
0 
(5,1,4) 
4/4 
4/2 
4/2 
0 
4/4 
4/4 
(5,2,6) 
0 
6/2 
0 
6/6 
0 
6/2 
(5,3,24) 
0 
0 
0 
24/6 
24/8 
0 
,
and thus the analog of the KramerMesner matrix turns out to be