Abstract
Quasi-symmetric designs with block intersection numbers 0 and y⩾2 are considered. It is shown that the number of such designs is finite under any one of the following two restrictions: (1) The block size k is fixed. (2) The integer pair ( e, z ), with the following property is fixed: the number of blocks disjoint from a given block is at most e and the positive block intersection number y is at most z. The connection of these results with a well-known conjecture on symmetric designs is discussed.
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