I have a vinyl record that says it has been digitally remastered - this would mean that there is no true analogue wave anymore. One reason I still have and buy vinyl albums is because they are supposed to be analogue. Is the digital wave on a remastered vinyl any better than a CD (44kHz/16bit) or would it be something closer to the studio quality digital audio?
Analogue medium do technically have a higher dynamical range than digital due to the nature of being analogue ("atom"-level wave description, although you have material limitations of the material vinyl itself, but still). If the human ear can hear the difference of a 24-bit digital version of it, or even a 16-bit version, is of course open for debate.
If the content on the vinyl has been digitally re-mastered the dynamic range of the analogue version would naturally have been capped off. The main purpose however is to remove hiss, noise, improve spatial and EQ area and such. Putting it back on vinyl you will still not be able to avoid static electricity and other "flaws" of the vinyl medium so in my opinion it is not necessary better if the original recording, provided it was all analogue, sounded good as it was.
If it has been digitally (re)mastered it will sound "better" (technically speaking as this will be a matter of opinion) on CD as the benefits of analogue (mainly dynamic range) is gone.
(Also as a side-note, the best mastering engineers uses analogue processing such as tape-saturation in their chain, but you will end up digital at the end nowadays. However, the membrane of the loudspeaker will remain analogue - nothing will change that for a while).
the "digital remastering" itself is not a problem. the year it was done and by who will affect whether it became a problem in a specific instance.
if you can get a mint copy of an original issue vinyl album, it's often nicer sounding, but it depends on your taste of course and your reference points. the digital vs analog aspect of remastering especially these days is of immeasurable consequence to the quality of the master or any copies of any music.
if you can't just listen to a copy and judge if you like it or that it's made well, but you want to avoid later realising you bought a dud copy of something when your perception improves or you hear a better copy, then all you have to go by is what you know or what your experience has been with the label, studio, era and engineers involved. for example, an album remastered by universal in the past 10 years is probably terrible, unless it's from universal france in which case it might be great depending on who worked on it, have a listen. stuff form japan is probably incredible from any issuer any year, etc.
to elaborate on why.. good engineers will have made high definition masters 96kHz * 24bit and not made the audio to fit the digital format constraints, but instead processed the signal for the constraints of the vinyl disc cutting and playback, and done that with analogue processes (a whole other big q and a), and the guy cutting the disc will have a good lathe, head, tip and a lot of experience.
re the technicalities if it puts your mind at ease --tho it probably won't-- ...
in digital audio you have a sudden absolute limit to bandwidth occurring just before half of the sample / clock rate for playback. this is done using a sync filter combined with some other filtering. there is a small amount of intermodulation with that clock rate as a result of the impossibility of making ideal filters and other imperfections. also if you have very high frequency information and digital masters are not made very well --and most are not-- you will get overshooting and distortion in playback and other nasty sounds. some like the nastiness, some don't. there are always varying amounts of alias frequencies due to all this, scattered thru your final digital audio, making it a touch cloudy and digital sounding. these things are the trade offs of digital. in the end tho, typical dynamic range and bandwidth for consumer grade digital is around 93dB +/-3dB from 0Hz to 19kHz, roughly, or way more than double that for higher resolutions like 96kHz 24bit or other resolutions used professionally. unfortunately to cover all bases in this explanation would require writing a book and if you really care to understand it, you will need devote a few years of your life to studying and working with it.
in contrast to the constraints of the digital system, stereo vinyl has a dynamic range which is extremely complicated to explain and define, and varies by sooo many factors but typically it falls off in the center of the stereo image by 6dB from around 2kHz heading up and down the spectrum, tapering off further at 500Hz and around 13kHz around the outer perimeter of the disc at 33rpm when the disc is virgin, also taper off even further at 50Hz and don't think about having anything around that frequency in the stereo field, the range is also limited further in all dimensions depending on stereo content and how much energy at what frequencies is in the left or right channel. and now consider at best you have around 80dB of range at that ideal point in the mids in the center of the stereo image, due to surface noise and other systemic noise. tho this varies hugely depending on cutting and playback systems and actual content of the signal cut to disc, the system is highly non linear in every respect but the distortions and noise do help to disguise other nasties that are otherwise revealed in the audio, like tape hiss or digital distortions, what have you, and all this ends up sounding nice to people who listen to and like the sound of vinyl.
so yeah, whatever really. the music and the particular product are what count. not whether something was / is digital or analog.
I'd like to take an Occam's Razor approach to this question:
Maybe the mastering engineer on the original didn't do such a great job or it could simply mean the press wasn't that great (each stamper is only good per 1000 presses, and degrades with each successive stamp). If it was recycled vinyl versus virgin vinyl, well, the press is pretty much screwed before it's finished. As such, the final vinyl output maybe wasn't all that great.
So, the best copy they find might have been carefully digitized, re-mastered within the digital/DAW domain (re-EQed, dynamics correction, stereo imaging/phasing correction, etc), and then carefully taken through a new vinyl pressing process again with great precision for a better, more definitive product, "digitally remastered".
Source: As a former House DJ and still House enthusiast, I do this all the time with all vinyl I buy (well, except the re-pressing). White labels are notorious for being not that great of presses, and usually need to be digitized at a high sample rate into the digital domain, and re-mastered for optimal fidelity. In this case, the resulting digitally-stored file (after digitally-remastering) will sound miles better than the original vinyl.