  This paper determines the range of feasible values of standard error
exponents for binary-input memoryless symmetric channels of fixed capacity $C$
and shows that extremes are attained by the binary symmetric and the binary
erasure channel. The proof technique also provides analogous extremes for other
quantities related to Gallager's $E_0$ function, such as the cutoff rate, the
Bhattacharyya parameter, and the channel dispersion.
