Abstract
For Turán's (3, 4)-conjecture, in the case of $n = 3k+1$ vertices, ${1 \over 2}6^{k-1}$ non-isomorphic hypergraphs are constructed that attain the conjecture. In the case of $n = 3k+2$ vertices, $6^{k-1}$ non-isomorphic hypergraphs are constructed that attain the conjecture.
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