Some of the BIBDs given by Furino could be halved in size. The larger subgroup used by the OBIBDs is of the form B = {C, -C} in nearly all cases so far found, the only exception being with groups of orders {2,3,4,6,12}. In other words, the ability to construct OBIBDs seems to be confined to those cases where Furino could halve the design size. So, the OBIBD can be split into two as with BIBDs, with blocks {C,-C} being twinned with blocks {-C,C}, as it were, though the individual plot pairs don't agree. The question is, therefore, can the OBIBD be halved accordingly? This has yet to be investigated.

Adding a pair 0,0 (or the equivalent in the ring being used) to each block, gives a pergola/OBIBD with a larger block size. This is the second type of OBIBD described in the definitions.

Galois Rings are defined as direct sums of Galois Fields. Where the multiplicative subgroups of the Galois Fields have subgroups of the same order, then the conditions of the general theorem apply. Thus the examples include a design with v = 91, where the ring is GF(7)⊕GF(13). GF(7) and GF(13) each contain subgroups of order 6, allowing an OBIBD with block size 3 to be constructed. See the examples. By adding a pair (0,0),(0,0) to each block, a design with block size 4 can be constructed, as mentioned in the previous note.