# on broadcast encryption

I've read the following paper and have one question on it.

M. Luby and J. Staddon, "Combinatorial Bounds for Broadcast Encryption", EUROCRYPT'98.

On page 523 (12th page of the paper) the authors say

…there are at most $2^{tm}$ petals in $\mathcal{F}$ which don't split any of the blocks, $L_i$.

However, I don't know how they can derive the number $2^{tm}$. Probably I missed something very easy, but anyway I can't understand. Anyone here can help me?