  Fingerprinting enables two parties to infer whether the messages they hold
are the same or different when the cost of communication is high: each message
is associated with a smaller fingerprint and comparisons between messages are
made in terms of their fingerprints alone. In the simultaneous message passing
model, it is known that fingerprints composed of quantum information can be
made exponentially smaller than those composed of classical information. For
small message lengths, we present constructions of optimal classical
fingerprinting strategies with one-sided error, in both the one-way and
simultaneous message passing models, and provide bounds on the worst-case error
probability with the help of extremal set theory. The performance of these
protocols is then compared to that for quantum fingerprinting strategies
constructed from spherical codes, equiangular tight frames and mutually
unbiased bases.
