In the paper the give the address of the electronic form of the catalog
of the 14k stars. IIRC this goes to about 140 ly, within this distance
I estimate there are about 3x that many stars. This is a guess based
on the Initial Mass Function ( more K & M stars, fewer OBAs ), but
it is only a guess. Based on this a complete catalog to 300 ly would
have about 330k entries.
An attempt to exhaustively survey _all_ stars down through M-type subdwarves
within a mere 10 parsecs (~32.6 ly) of Sol is curently being carried out
by the RECONS group: http://www.chara.gsu.edu/RECONS/. To detect stars
out to 300 ly would obviously be much harder, since they would be up to
~100 times dimmer, and there will be ~1000 times as many stars to survey.
The 2MASS survey is attempting to detect all objects brighter than
1 mJy in the J, H, and K_s infrared bands,
http://www.ipac.caltech.edu/2mass/overview/about2mass.html;
this survey will hopefully detect many nearby L- and T-type brown dwarves,
http://www.ipac.caltech.edu/2mass/overview/dwarfs.html.
but will represent an exhaustive survey of them.