In recent years, several methods have been proposed for constructing -optimal and minimax-optimal supersaturated designs (SSDs). However, until now the enumeration problem of such designs has not been yet considered. In this paper, -optimal and minimax-optimal k-circulant SSDs with 6, 10, 14, 18, 22, and 26 runs, factors and are enumerated in a computer search. We have also enumerated all -optimal and minimax-optimal k-circulant SSDs with (mod 4) and . The computer search utilizes the fact that theses designs are equivalent to certain 1-rotational resolvable balanced incomplete block designs. Combinatorial properties of these resolvable designs are used to restrict the search space.