Abstract
It is unknown whether a BIB design with parameters (22, 33, 12, 8, 4) exists or not. In this paper, a necessary condition for the block structure of BIB designs is given. Using this necessary condition, it is shown that the intersection numbers { n i } for any block in any BIB design with parameters (22, 33, 12, 8, 4) must be one of the four types shown in Table I if the BIB design exists. It is also shown that if there exists a BIB design with parameters (22, 33, 12, 8, 4), the BIB design must contain at least one block of Type 1 or 3 in Table I.
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