How to convert an MTS file without loosing quality?
What is your definition of huge and what is your definition of high quality?  Size is directly related to compression and compression is directly inversely related to quality for the most part.  

Some amount of compression can be had for free using lossless compression or near free with more efficient pattern finding for lossy compression, but for the most part, there is a direct relationships between size and quality.

In fact, you generally have to actually increase the size to maintain the quality when re-encoding a lossy file as information that was already lost by the first can't be recovered, but other information may be lost due to the encoding process running again, so the combined error requires a higher data rate to avoid losing more.

MTS files are already generally based on H.264 (MPEG4) and are generally relatively small.  It should be possible to extract the MPEG4 from the container and repackage without any loss, but to reduce size would pretty much require a reduction in quality.