... 1}, then Q(R) as definedin Section 2 is the Cayley table of the group Q × R represented on {0, 1, . . . , mn − 1}.Thus, if Q is taken as the Cayley table of C2, then the square Q(Q) gives the ... either contained in precisely one tripleor one group, but not both. The vertices of the embedded graph Kn,n,nform the pointsof each design, the tripartition determines the groups, and the ... introduces a notationfor the resulting squares A and A′to emphasize their dependency on L, L′, Q and Q′. The corollary and the notation will be useful in the subsequent section. the electronic journal...