As early as 1924 H.Nyquist realised the existance of a fundamental limit and derived an equation expressing the maximum data rate for a finite bandwidth noiseless channel.

Maximum data rate = 2 * H * LOGbase2 V bits/sec

Where H=bandwidth

V=number of levels

In 1948 C.Shannon carried Nyquists work further and used information theory to extend it to the case of a channel subject to random (thermal) noise.

Maximum data rate = H * LOGbase2 (1+S/N)

Where H=bandwidth

S/N = signal to noise ratio

For example a channel of 3000 Hz bandwidth and a signal to thermal noise ratio of 30dB can never transmit more than 30,000 bps, no matter how many or few signal levels are used and no matter how often or how infrequent samples are taken.

In practice it is difficult to even approach the Shannon limit, a bit rate of 9600 on a voice-grade line is good.