Some New Symmetric Block Designs EDWARD

In his book [I 1, Marshall Hall gives a table of balanced incomplete block designs with from 3 to 15 replications. It is mentioned there that a solution is unknown as to whether or not there exists a symmetric block design with parameters (v, k, h) = (36, 15, 6) (number 104 in the table). It is the purpose of this paper to show that such a design can in fact be constructed quite simply and to suggest that a more general construction might exist for designs with parameters (0, k, A) = (4u2, 2u2 u, u2 u). The above design is obtained by taking u = 3. In the case u = 2’ such designs have already been constructed [2], the designs being in fact group difference sets.