  We consider strong external difference families (SEDFs); these are external
difference families satisfying additional conditions on the patterns of
external diferences that occur, and were first defined in the context of
classifying optimal strong algebraic manipulation detection codes. We establish
new necessary conditions for the existence of (n; m; k; lambda)-SEDFs; in
particular giving a near-complete treatment of the lambda = 2 case. For the
case m = 2, we obtain a structural characterization for partition type SEDFs
(of maximum possible k and lambda), showing that these correspond to Paley
partial difference sets. We also prove a version of our main result for
generalized SEDFs, establishing non-trivial necessary conditions for their
existence.
