The fine structures of three pairwise distinct Latin squares

Let Lk=(aij(k))v×v, k=1,2,3 be Latin squares on symbol set S containing v elements. The fine structure of three Latin squares L1,L2,L3 is defined to be (t,s) if s=v2-c1 and t=c2, where cl is the number of cells (i,j) such that |{aij(1),aij(2),aij(3)}|=l for l=1,2. Denote by Fin*(v) the set of all integer pairs (t,s) for which there exist three pairwise distinct Latin squares of order v on the same set having fine structure (t,s). We determine the set Fin*(v) for any positive integer v⩾8.