A Conjecture about BIBDs

The conjecture: “If the case (v,k) = (8, 3) is the only one where the trivial balanced incomplete block design (BIBD) is elementary” is formulated. It is supported by the theorem: Theorem The conjecture is correct if at least one of the following conditions holds: v < 26, k < 6, for v > 8 if v is prime or a prime power.

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