Note
All directed BIBDs with k = 3 exist

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Abstract

A directed BIBD with parameters (υ, b, r, k, λ) is a BIBD with parameters (υ, b, r, k, 2λ) in which each ordered pair of varieties occurs together in exactly λ blocks. It is shown that λυ(υ − 1) ≡ 0 (mod 3) is a necessary and sufficient condition for the existence of a directed (υ, b, r, k, λ) BIBD with k = 3.

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