ABSTRACT
Consider the design that contains the blocks {1, 2, 4}, {1,2,5},{1,3,4},{1,3,6}, {2, 3, 5}, {2, 3, 6}, {4, 5, 6}, {4, 5, 6}. Even though λ1 = λ2, the first and second associate classes cannot be combined since if they could, then 1 would have first associates 2, 3, and 4; 2 would have first associates 1, 3, and 5; 4 would have first associates 1, 5, and 6. Then p111 = 1 for first associates 1 and 2, and is 0 for first associates 1 and 4. But this number must be a constant, from the definition of an association scheme. See §VI.1 for definitions pertaining to association schemes.
