Reconstruction of shamir secret shares in the presence of malicious parties

Suppose we have a (t,n) Shamir-secret sharing scheme. A value of some computation is shared with n parties where at most $t-1$ parties are malicious. What is the best strategy to reconstruct the shares? I believe we can use Reed-Solomon error corrections to retrieve value for upto t<n/3. For t<n/2, we can randomly reconstruct $k$ times using $t$ shares and check for the value that appears the most number of times. Is there anything better than this?

A stronger approach is to use the Guruswami-Sudan list-decoding algorithm. If you have $m$ shares then their polynomial reconstruction algorithm will return all polynomials of degree at most $t$ such that at least $k$ of the shares satisfy the polynomial, provided that $k>\sqrt{km}$. As $m-t+1$ grows relative to $t$, the number of sporadic false positives will reduce (notice that if the number of honest parties is close to the number of dishonest parties, there is a significant chance that we cannot uniquely recover the polynomial but can contain it to a relatively short list of possibilities).