Sets Used in Proof of Theorem 10

\hat{T}_{1_6} = {(0 0 0 0 0 0), (0 0 0 0 1 1), (0 0 0 1 0 0), (0 0 0 1 1 0), 
                  (0 0 1 0 1 1), (0 0 1 1 0 0), (0 0 1 1 0 1), (0 0 1 1 1 1), 
                  (0 1 0 0 0 1), (0 1 0 1 0 0), (0 1 0 1 0 1), (0 1 0 1 1 1), 
                  (0 1 1 0 0 0), (0 1 1 0 0 1), (0 1 1 0 1 0), (0 1 1 1 1 0), 
                  (1 0 0 0 0 1), (1 0 0 0 1 0), (1 0 0 1 0 1), (1 0 0 1 1 1),
                  (1 0 1 0 0 0), (1 0 1 0 0 1), (1 0 1 0 1 0), (1 0 1 1 1 0),
                  (1 1 0 0 0 0), (1 1 0 0 1 0), (1 1 0 0 1 1), (1 1 0 1 1 0), 
                  (1 1 1 0 1 1), (1 1 1 1 0 0), (1 1 1 1 0 1), (1 1 1 1 1 1)},

\hat{T}_{2_6} = {(0 0 0 0 0 1), (0 0 0 0 1 0), (0 0 0 1 0 1), (0 0 0 1 1 1),
                 (0 0 1 0 0 0), (0 0 1 0 0 1), (0 0 1 0 1 0), (0 0 1 1 1 0),
                 (0 1 0 0 0 0), (0 1 0 0 1 0), (0 1 0 0 1 1), (0 1 0 1 1 0),
                 (0 1 1 0 1 1), (0 1 1 1 0 0), (0 1 1 1 0 1), (0 1 1 1 1 1),
                 (1 0 0 0 0 0), (1 0 0 0 1 1), (1 0 0 1 0 0), (1 0 0 1 1 0), 
                 (1 0 1 0 1 1), (1 0 1 1 0 0), (1 0 1 1 0 1), (1 0 1 1 1 1),
                 (1 1 0 0 0 1), (1 1 0 1 0 0), (1 1 0 1 0 1), (1 1 0 1 1 1), 
                 (1 1 1 0 0 0), (1 1 1 0 0 1), (1 1 1 0 1 0), (1 1 1 1 1 0)}.  

T_{1_6} = {(0 0 1 0 0 1), (0 0 0 0 0 0), (0 0 0 0 1 1), (0 0 0 1 0 0), 
           (0 0 0 1 1 0), (0 0 1 0 1 1), (0 0 1 1 0 0), (0 0 1 1 1 1), 
           (0 1 0 0 0 1), (0 1 0 1 0 0), (0 1 0 1 0 1), (0 1 0 1 1 1), 
           (0 1 1 0 0 0), (0 1 1 0 0 1), (0 1 1 0 1 0), (0 1 1 1 1 0),
           (1 0 0 0 0 1), (1 0 0 0 1 0), (1 0 0 1 0 1), (1 0 0 1 1 1), 
           (1 0 1 0 0 0), (1 0 1 0 0 1), (1 0 1 0 1 0), (1 0 1 1 1 0),
           (1 1 0 0 0 0), (1 1 0 0 1 0), (1 1 0 0 1 1), (1 1 0 1 1 0), 
           (1 1 1 0 1 1), (1 1 1 1 0 0), (1 1 1 1 0 1), (1 1 1 1 1 1)},

T_{2_6} = {(0 0 1 1 0 1), (0 0 0 0 0 1), (0 0 0 0 1 0), (0 0 0 1 0 1),
           (0 0 0 1 1 1), (0 0 1 0 0 0), (0 0 1 0 1 0), (0 0 1 1 1 0), 
           (0 1 0 0 0 0), (0 1 0 0 1 0), (0 1 0 0 1 1), (0 1 0 1 1 0), 
           (0 1 1 0 1 1), (0 1 1 1 0 0), (0 1 1 1 0 1), (0 1 1 1 1 1),
           (1 0 0 0 0 0), (1 0 0 0 1 1), (1 0 0 1 0 0), (1 0 0 1 1 0), 
           (1 0 1 0 1 1), (1 0 1 1 0 0), (1 0 1 1 0 1), (1 0 1 1 1 1),
           (1 1 0 0 0 1), (1 1 0 1 0 0), (1 1 0 1 0 1), (1 1 0 1 1 1), 
           (1 1 1 0 0 0), (1 1 1 0 0 1), (1 1 1 0 1 0), (1 1 1 1 1 0)}

\hat{T}_{1_7} = {(0 0 0 0 0 0 0), (0 0 0 0 0 1 1), (0 0 0 0 1 0 0), (0 0 0 0 1 1 0),
                 (0 0 0 1 0 0 1), (0 0 0 1 0 1 1), (0 0 0 1 1 0 0), (0 0 0 1 1 1 1),
                 (0 0 1 0 0 0 1), (0 1 0 1 0 0),   (0 0 1 0 1 0 1), (0 0 1 0 1 1 1), 
                 (0 0 1 1 0 0 0), (0 0 1 1 0 0 1), (0 0 1 1 0 1 0), (0 0 1 1 1 1 0),
                 (0 1 0 0 0 0 1), (0 1 0 0 0 1 0), (0 1 0 0 1 0 1), (0 1 0 0 1 1 1), 
                 (0 1 0 1 0 0 0), (0 1 0 1 0 0 1), (0 1 0 1 0 1 0), (0 1 0 1 1 1 0),
                 (0 1 1 0 0 0 0), (0 1 1 0 0 1 0), (0 1 1 0 0 1 1), (0 1 1 0 1 1 0), 
                 (0 1 1 1 0 1 1), (0 1 1 1 1 0 0), (0 1 1 1 1 0 1), (0 1 1 1 1 1 1), 
                 (1 0 0 0 0 0 0), (1 0 0 0 0 1 1), (1 0 0 0 1 0 0), (1 0 0 0 1 1 0), 
                 (1 0 0 1 0 0 1), (1 0 0 1 0 1 1), (1 0 0 1 1 0 0),   (1 0 1 1 1 1), 
                 (1 0 1 0 0 0 1), (1 0 1 0 1 0 0), (1 0 1 0 1 0 1), (1 0 1 0 1 1 1), 
                 (1 0 1 1 0 0 0), (1 0 1 1 0 0 1), (1 0 1 1 0 1 0), (1 0 1 1 1 1 0),
                 (1 1 0 0 0 0 1), (1 1 0 0 0 1 0), (1 1 0 0 1 0 1), (1 1 0 0 1 1 1), 
                 (1 1 0 1 0 0 0), (1 1 0 1 0 0 1), (1 1 0 1 0 1 0), (1 1 0 1 1 1 0),
                 (1 1 1 0 0 0 0), (1 1 1 0 0 1 0), (1 1 1 0 0 1 1), (1 1 1 0 1 1 0), 
                 (1 1 1 1 0 1 1), (1 1 1 1 1 0 0), (1 1 1 1 1 0 1), (1 1 1 1 1 1 1)}

\hat{T}_{2_7} = {(0 0 0 0 0 0 1), (0 0 0 0 0 1 0), (0 0 0 0 1 0 1), (0 0 0 0 1 1 1),
                 (0 0 0 1 0 0 0), (0 0 0 1 0 1 0), (0 0 0 1 1 0 1), (0 0 0 1 1 1 0), 
                 (0 0 1 0 0 0 0), (0 0 1 0 0 1 0), (0 0 1 0 0 1 1), (0 0 1 0 1 1 0),
                 (0 0 1 1 0 1 1), (0 0 1 1 1 0 0), (0 0 1 1 1 0 1), (0 0 1 1 1 1 1),
                 (0 1 0 0 0 0 0), (0 1 0 0 0 1 1), (0 1 0 0 1 0 0), (0 1 0 0 1 1 0), 
                 (0 1 0 1 0 1 1), (0 1 0 1 1 0 0), (0 1 0 1 1 0 1), (0 1 0 1 1 1 1), 
                 (0 1 1 0 0 0 1), (0 1 1 0 1 0 0), (0 1 1 0 1 0 1), (0 1 1 0 1 1 1),
                 (0 1 1 1 0 0 0), (0 1 1 1 0 0 1), (0 1 1 1 0 1 0), (0 1 1 1 1 1 0), 
                 (1 0 0 0 0 0 1), (1 0 0 0 0 1 0), (1 0 0 0 1 0 1), (1 0 0 0 1 1 1), 
                 (1 0 0 1 0 0 0), (1 0 0 1 0 1 0), (1 0 0 1 1 0 1), (1 0 0 1 1 1 0), 
                 (1 0 1 0 0 0 0), (1 0 1 0 0 1 0), (1 0 1 0 0 1 1), (1 0 1 0 1 1 0),
                 (1 0 1 1 0 1 1), (1 0 1 1 1 0 0), (1 0 1 1 1 0 1), (1 0 1 1 1 1 1), 
                 (1 1 0 0 0 0 0), (1 1 0 0 0 1 1), (1 1 0 0 1 0 0), (1 1 0 0 1 1 0), 
                 (1 1 0 1 0 1 1), (1 1 0 1 1 0 0), (1 1 0 1 1 0 1), (1 1 0 1 1 1 1), 
                 (1 1 1 0 0 0 1), (1 1 1 0 1 0 0), (1 1 1 0 1 0 1), (1 1 1 0 1 1 1),
                 (1 1 1 1 0 0 0), (1 1 1 1 0 0 1), (1 1 1 1 0 1 0), (1 1 1 1 1 1 0)}.

T_{1_7} = {(0 0 0 0 0 0 0), (0 0 0 0 0 1 1), (0 0 0 0 1 0 0), (0 0 0 0 1 1 0),
           (0 0 0 1 0 0 1), (0 0 0 1 0 1 1), (0 0 0 1 1 0 0), (0 0 0 1 1 1 1),
           (0 0 1 0 0 0 1), (0 1 0 1 0 0),   (0 0 1 0 1 0 1), (0 0 1 0 1 1 1), 
           (0 0 1 1 0 0 0), (0 0 1 1 0 0 1), (0 0 1 1 0 1 0), (0 0 1 1 1 1 0),
           (0 1 0 0 0 0 1), (0 1 0 0 0 1 0), (0 1 0 0 1 0 1), (0 1 0 0 1 1 1),
           (0 1 0 1 0 0 0), (0 1 0 1 0 0 1), (0 1 0 1 0 1 0), (0 1 0 1 1 1 0),
           (0 1 1 0 0 0 0), (0 1 1 0 1 0 0), (0 1 1 0 0 1 1), (0 1 1 0 1 1 0), 
           (0 1 1 1 0 1 1), (0 1 1 1 1 0 0), (0 1 1 1 1 0 1), (0 1 1 1 1 1 1), 
           (1 0 0 0 0 0 0), (1 0 0 0 0 1 1), (1 0 0 0 1 0 0), (1 0 0 0 1 1 0), 
           (1 0 0 1 0 0 1), (1 0 0 1 0 1 1), (1 0 0 1 1 0 0),   (1 0 1 1 1 1),
           (1 0 1 0 0 0 1), (1 0 1 0 1 0 0), (1 0 1 0 1 0 1), (1 0 1 0 1 1 1), 
           (1 0 1 1 0 0 0), (1 0 1 1 0 0 1), (1 0 1 1 0 1 0), (1 0 1 1 1 1 0),
           (1 1 0 0 0 0 1), (1 1 0 0 0 1 0), (1 1 0 0 1 0 1), (1 1 0 0 1 1 1),
           (1 1 0 1 0 0 0), (1 1 0 1 0 0 1), (1 1 0 1 0 1 0), (1 1 0 1 1 1 0),
           (1 1 1 0 0 0 0), (1 1 1 0 0 1 0), (1 1 1 0 0 1 1), (1 1 1 0 1 1 0), 
           (1 1 1 1 0 1 1), (1 1 1 1 1 0 0), (1 1 1 1 1 0 1), (1 1 1 1 1 1 1)}

T_{2_7} = {(0 0 0 0 0 0 1), (0 0 0 0 0 1 0), (0 0 0 0 1 0 1), (0 0 0 0 1 1 1),
           (0 0 0 1 0 0 0), (0 0 0 1 0 1 0), (0 0 0 1 1 0 1), (0 0 0 1 1 1 0), 
           (0 0 1 0 0 0 0), (0 0 1 0 0 1 0), (0 0 1 0 0 1 1), (0 0 1 0 1 1 0),
           (0 0 1 1 0 1 1), (0 0 1 1 1 0 0), (0 0 1 1 1 0 1), (0 0 1 1 1 1 1),
           (0 1 0 0 0 0 0), (0 1 0 0 0 1 1), (0 1 0 0 1 0 0), (0 1 0 0 1 1 0), 
           (0 1 0 1 0 1 1), (0 1 0 1 1 0 0), (0 1 0 1 1 0 1), (0 1 0 1 1 1 1), 
           (0 1 1 0 0 0 1), (0 1 1 0 0 1 0), (0 1 1 0 1 0 1), (0 1 1 0 1 1 1), 
           (0 1 1 1 0 0 0), (0 1 1 1 0 0 1), (0 1 1 1 0 1 0), (0 1 1 1 1 1 0), 
           (1 0 0 0 0 0 1), (1 0 0 0 0 1 0), (1 0 0 0 1 0 1), (1 0 0 0 1 1 1), 
           (1 0 0 1 0 0 0), (1 0 0 1 0 1 0), (1 0 0 1 1 0 1), (1 0 0 1 1 1 0), 
           (1 0 1 0 0 0 0), (1 0 1 0 0 1 0), (1 0 1 0 0 1 1), (1 0 1 0 1 1 0),
           (1 0 1 1 0 1 1), (1 0 1 1 1 0 0), (1 0 1 1 1 0 1), (1 0 1 1 1 1 1),
           (1 1 0 0 0 0 0), (1 1 0 0 0 1 1), (1 1 0 0 1 0 0), (1 1 0 0 1 1 0), 
           (1 1 0 1 0 1 1), (1 1 0 1 1 0 0), (1 1 0 1 1 0 1), (1 1 0 1 1 1 1), 
           (1 1 1 0 0 0 1), (1 1 1 0 1 0 0), (1 1 1 0 1 0 1), (1 1 1 0 1 1 1), 
           (1 1 1 1 0 0 0), (1 1 1 1 0 0 1), (1 1 1 1 0 1 0), (1 1 1 1 1 1 0)}.