Assume that a unit hypercube is given as [ 0 , 1 ] d, that is, the range is [ 0 , 1 ] in each dimension. The main diagonal in the hypercube is defined as the vector from ( 0 , 0 ) =( 0 , . . . , 0 ⏟ d − 1 , 0 ) to ( 1 , 1 ) =( 1 , . . . , 1 ⏟ d − 1 , 1 ). For example, when d = 2, the main diagonal goes from ( 0 , 0 ) to ( 1 , 1 ). On the other hand, the main anti-diagonal is defined as the vector from ( 1 , 0 ) = ( 1 , . . . , 1 ⏟ d − 1 , 0 ) to ( 0 , 1 ) = ( 0 , . . . , 0 ⏟ d − 1 , 1 ). For example, for d = 2, the anti-diagonal is from ( 1 , 0 ) to ( 0 , 1 ).