The Jargon File (version 4.4.7, 29 Dec 2003):

paper-net
 n.

    Hackish way of referring to the postal service, analogizing it to a very
    slow, low-reliability network. Usenet sig blocks sometimes include a ?
    Paper-Net:? header just before the sender's postal address; common variants
    of this are ?Papernet? and ?P-Net?. Note that the standard netiquette
    guidelines discourage this practice as a waste of bandwidth, since netters
    are quite unlikely to casually use postal addresses. Compare voice-net, 
    snail-mail.


The Free On-line Dictionary of Computing (30 December 2018):

snail mail
papermail
paper-net

    (Or "snailmail", "smail" from "US Mail" via
   "USnail"; "paper mail").  Bits of dead tree sent via the
   postal service as opposed to electronic mail.  One's postal
   address is, correspondingly, a "snail (mail) address".  There
   have even been parody USnail posters and stamps made.

   The variant "paper-net" is a hackish way of referring to the
   postal service, comparing it to a very slow, low-reliability
   network.  Sig blocks sometimes include a "Paper-Net:"
   header just before the sender's postal address; common
   variants of this are "Papernet" and "P-Net".  Note that the
   standard netiquette guidelines discourage this practice as a
   waste of bandwidth, since netters are quite unlikely to
   casually use postal addresses and if they really wanted your
   snail mail address they could always ask for it by e-mail.

   Compare voice-net, sneakernet, P-mail.

   (1995-01-31)