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Since a $1$-CFF is the same as a Sperner family, using Sperner's theorem, we get $t(1, n) \\sim \\log_{2}(n)$ as $n$ grows. Erd\\\"os, Frankl, and F\\\"uredi (JCTA, 1982) proved that $3.106\\log_{2}(n) < t(2,n) < 5.512\\log_{2}(n)$. 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