Bounds on the Probability of Undetected Error

New upper and lower bounds are obtained for the probability of undetected error for block codes in a binary symmetrical channel (BSC). These bounds improve the available bounds by a factor that increases exponentially with the block length $n$, provided that the transmission rate is fixed and does not exceed the capacity of the BSC. The resultant bounds are used to select the parameters of a quasioptimal code for transmission over a BSC with instantaneous and noiseless feedback.