Incompatibilities in sampling rates/bit rates(MP3)[SOLVED]

Hello everyone.

I am user of windows 7, I use Audacity 2.0.5 which I downloaded in its zip version.

I am doing a non-musical project and I have several mono .wav files (65536 samples/sec and 16 bits/sample) which I have resampled to the following sampling rates:
8000 Hz, 16000 Hz, 24000 Hz, 44100 Hz and 48000 Hz.

For each sampling frequency (6 in total, considering the original file also) I need to compressed into MP3 CBR with each of the following bitrates:
8 kbps, 64 kbps, 128 kbps, 256 kbps and 320 kbps.

All in all, I need to create the 30 possible combinations between the sampling rates and the MP3 bitrates.

The problem I have is that when compressing into MP3 there seem to be certain incompatibilities between my current sampling rate and the bitrate I want to get. Audacity asks me for resampling into different values before, but due to the nature of my project, I cannot do that.

As far as I am concerned bitrate= nºchannels x sampling rate x bits per sample. My thought was that these incompatibilities might be produced due to the number of bits per sample neccessary to get the desire bitrate. For that reason I created the following table, with both compatibilities and incompatibilities between the sampling rates and bitrates with the neccesary number of bits for each match (just bitrate/sampling rate). This table is attached in this post. It also shows the sampling rates Audacity gives as possibility when asking for resampling if the compression cannot be done. Otherwise an OK! is showed.

The results I have got make no sense for me. For example, for the match 8000 Hz, and 128 kbps, the necessary number of bits is 16 and the compression can be done with no problems. However, for 16000 Hz and and 256 kbps, also 16 bits per sample are required, but Audacity asks for resampling.

Can someone help me to clarify the incompatibilities I have got. Thanks in advance!
necessary bits.JPG

That is only for uncompressed formats.

As you can see from the below MP3 specification, 16000 Hz and 256 kbps is not a legal combination. A higher sample rate is required for such a high bit rate.

Try it at the command-line. LAME will force the bit rate down to 160 kbps.

MPEG-1 layer III sample frequencies (kHz): 32 48 44.1:
bit rates (kbps): 32 40 48 56 64 80 96 112 128 160 192 224 256 320

MPEG-2 layer III sample frequencies (kHz): 16 24 22.05:
bit rates (kbps): 8 16 24 32 40 48 56 64 80 96 112 128 144 160

MPEG-2.5 layer III sample frequencies (kHz): 8 12 11.025:
bit rates (kbps): 8 16 24 32 40 48 56 64 80 96 112 128 144 160


Thank you Gale. Perfect answer. Very useful.