Bit optimal distributed consensus

The Distributed Consensus problem involves n processors each of which holds an initial binary value. At most t processors may be faulty and ignore any protocol (even behaving maliciously), yet it is required that non-faulty processors eventually agree on a common value that was initially held by one of them. The quality of a consensus protocol is measured using the following parameters: the number of processors n, the number of rounds of message exchange r and the total number of bits transmitted B. The known lower bounds are respectively 3t + 1, t + 1 and Ω(nt).