(i) each of the treatments occurs in r blocks,
(ii) there exists an abstract relation between treatments satisfying the following:
(a) two treatments are either 1st, 2nd or 3rd associates, the relation of association being symmetrical i.e., if treatment a is the ith associate of b, then b is also the ith associate of a (i = 1, 2, 3),
(b) each treatment has exactly ni ith associates, and
(c) given any two treatments that are mutually ith associates, the number of treatments common to the jth associates of the first and kth associates of the second is (i, j, k = 1, 2, 3).
(iii) two treatments that are mutually ith associates occur together in exactly li blocks.