  In this work, a new lower bound for the maximal error probability of a
two-user discrete memoryless (DM) multiple-access channel (MAC) is derived.
This is the first bound of this type that explicitly imposes independence of
the users' input distributions (conditioned on the time-sharing auxiliary
variable) and thus results in a tighter sphere-packing exponent when compared
to the tightest known exponent derived by Haroutunian.
