Do deterministic secret sharing schemes exist?
Any deterministic secret sharing scheme as in the question has the property that any participant can run the deterministic algorithm for a guess of the shared secret, and eliminate the guess if the share that the algorithm deterministically assigns him/her does not match his/her share. This implies that some information about the secret is leaked in his/her share, or that his/her share is pointless (in the sense that his/her share can be removed from any set of shares that allows to reconstruct the secret, while keeping that ability).

Likely that's why there is no seldom such beast in the literature. For a counterexample to this assertion, see that other answer.