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This has to do with the maximum size of a datagram on the two machines involved. This depends on the sytems involved, and the MTU (Maximum Transmission Unit). According to "UNIX Network Programming", all TCP/IP implementations must support a minimum IP datagram size of 576 bytes, regardless of the MTU. Assuming a 20 byte IP header and 8 byte UDP header, this leaves 548 bytes as a safe maximum size for UDP messages. The maximum size is 65516 bytes. Some platforms support IP fragmentation which will allow datagrams to be broken up (because of MTU values) and then re-assembled on the other end, but not all implementations support this.
This information is taken from my reading of "UNIX Netowrk Programming" (see 1.6 Where can I get source code for the book [book title]?).
Andrew has pointed out the following regarding large UDP messages:
Another issue is fragmentation. If a datagram is sent which is too large for the network interface it is sent through, then the sending host will fragment it into smaller packets which are reassembled by the receiving host. Also, if there are intervening routers, then they may also need to fragment the packet(s), which greatly increases the chances of losing one or more fragments (which causes the entire datagram to be dropped). Thus, large UDP datagrams should be avoided for applications that are likely to operate over routed nets or the Internet proper.