Calabi-Yau Threefolds With Small Hodge Numbers
  We present a list of Calabi-Yau threefolds known to us, and with holonomy groups that are precisely SU(3), rather than a subgroup, with small Hodge numbers, which we understand to be those manifolds with height $(h^{1,1}+h^{2,1})\le 24$. With the completion of a project to compute the Hodge numbers of free quotients of complete intersection Calabi-Yau threefolds, most of which were computed in Refs. [1-3] and the remainder in Ref. [4], many new points have been added to the tip of the Hodge plot, updating the reviews by Davies and Candelas in Refs. [1, 5]. In view of this and other recent constructions of Calabi-Yau threefolds with small height, we have produced an updated list. 
Philip Candelas, Andrei Constantin, Challenger Mishra
hep-th math.AG