Some terms related to secret sharing: Optimality, What does it mean?
Optimality is actually not a well-defined term for secret sharing, and can refer to a number of different issues. First, one issue that is often considered is the size of the share that each party holds in the scheme. If the size of a party's share equals the size of the secret itself, then the secret sharing scheme is called ideal. (Formally, we don't talk about "size" but that the shares comes from the same domain as the secret.) Shamir's secret sharing scheme is ideal.

Other issues which come up are the threshold: how many parties are needed to reconstruct the secret versus against how many parties security holds, what the threshold is for active/passive security and so on. 

In short, the paper should define what they mean by optimal, and especially regarding what parameters.