Well, there are a number of methods of modulation.
In the Analog sense, there are phase, frequency and amplitude (that is, the carrier is changed by the modulating signal in one of those aspects). For the analog model, the carrier (to be effective) must be a higher frequency than the greatest offset caused by the modulating signal. In AM, this is the band of frequencies of the modulating signal. For frequency modulation, it depends on the characteristics of the modulator. For phase, it can be very low, but should be at least the bandwidth of the modulating signal (as phase modulation has some AM characteristics).
In the digital world, other techniques apply. The addition to a PRBS sequence (noted above) is actually used commonly to maintain a (statistically) constant bandwidth on the channel regardless of whether there is a signal present or not. It might be argued by some that is not really modulation, but that's another story.
There are other forms of digital modulation ( 8bit - 10 bit conversion is common) if we define modulation as making the signal suitable for the transmission medium ( normally it may be defined as imposing a variation onto one signal based on another - the modulating signal).
In the digital arena, the final output rate must be at least equal to the symbol rate of the modulating signal plus any overhead rate. Note I use the term symbol rate, not bit rate. The symbol rate is sometimes known (accurately) as baud rate, whereas bit rate and buad rate are not synonymous except for bits per symbol = 1. To avoid the common confusion over the term, symbol rate is more commonly used.
So there's a whole world of things to learn here - I suggest googling for some definitions.
Cheers
PeteS