Stepan Orevkov determined the braid index and found minimum width braid representatives for most of the links in LinkInfo. Lower bounds for the braid index were found using the Morton-Franks-Williams Inequality based on the Jones polynomial. In a few cases, this inequality was applied to the link with its components doubled, replacing each component with two parallel components. Computations were done using a program written by Morton and Short. Upper bounds were found be building explicit braid representatives; most of these could be done using [5]. The remaining cases were handled by using basic techniques to simplify given braid representatives.
[1] Orevkov, Stepan, Personal communication.