This protocol we describe uses 
communication for each
auctioneer. Information theory tells us that the bids must be 
in size. So, if we guarantee that t or fewer auctioneers can
obtain no information about the bids, each bidder must distribute
information to the auctioneers (which is 
per
auctioneer). The verifiable secret sharing methods actually require an
extra factor of 
above the theoretical minimums for
non-verifiable secret sharing. So, in total, just distributing the
bids requires 
communication for each auctioneer.
There are two major constant factors hidden by the notation which lie at the heart of high communication costs. The first is the large field we have chosen; the second is the constant associated with multiplying two polynomials. The choice of a large field was made to reduce the number of rounds of communicaiton required in phase 2, and alternative are being explored. The constant associated with multiplication is a more fundamental result of the distributed computation techniques used and the high fault-tolerance (3t<m) allowed.