So the grain is due to the fact that the scanner used to scan the image wasn't able to pick up as much detail as it should - or was it the fact that the print being scanned wasn't very large?
(Unless by 35mm Film scan you meant that the negatives were scanned
)
I read on wikipedia that with an excellent lens, high quality 35mm film could capture the equivalent of
22 megapixels per exposure. So theoretically if you get a large print and a high quality scanner, you should be able to transfer your images quite crisply?
It's not really grain. It's noise. The film scanner that did this is an older scanner that had a more limited dynamic range than the newer ones, so the shadow detail (what there was in the underexposed neg) was very difficult to extract. Some techniques since then are the multi-pass scans, something like doing HDR except via scanning for shadow detail with multiple scans while maintaining highlights.
Also, the scan was not a big scan, more like 2000x3000, converted to jpeg and resized probably several times before getting here.
My newer scanner is a Nikon Coolscan V, which has an improved dynamic range and can scan at 4000 dpi. If you figure a color scan of a full negative of 1" x 1.5" at full resolution that would be like 4000 X 6000 pixels (24meg) x 3 for NEF file or .tiff file, so it's way more than 22meg per exposure at highest resolution scan.
Bottom line: Some negatives are much trickier to scan than others. The best scans still come from professional drum scanners worth 1000's of dollars. And, grain ain't all bad, if it's really grain. Each film type has its own grain characteristics which gives it its "look." You really ought to take a look at some T-Max 3200 black and white prints. Done right, it's hard to duplicate the look, and it can be very creative. Anyway, that's another subject...
Noise is another matter, and is a digital thing.