Michael Barrus points out that Favaron, Maheo, and Sacle proved that residue, for instance, is always better than the Caro-Wei bound, and that an abstract of Jelen claims that residue is also better than Seklow’s bound. Mike wonders if anyone has compiled anything about the relations between the bounds we are using?
The answer is: we don’t know. For our purposes, there’s no reason for us to compute Caro-Wei or Seklow, as they won’t provide us any information that is not implied by the residue. They add unnecessary cycles to our computations. If we knew more information on the comparative effectiveness of the bounds we are using it would be both interesting and useful.