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.