Enumeration of E(s2)‐Optimal and Minimax‐Optimal Supersaturated Designs With 12 Rows, 11q Columns and smax=4

ABSTRACT The ‐optimal and minimax‐optimal supersaturated designs (SSDs) with 12 rows, columns, and are enumerated in a computer search: there are, respectively, 34, 146, 0, 3, and 1 such designs for , and 6. Cheng and Tang proved that for , there are no such SSDs. This completes the enumeration of all SSDs with the described restrictions. These results are obtained by enumerating the resolvable 2‐() designs such that any two blocks not in the same parallel class intersect in 2, 3, or 4 points, and the enumeration is carried out with a breadth‐first search algorithm over parallel classes with an isomorph rejection. The combinatorial properties of these resolvable designs restrict the search space. A consistency checking based on the principle of double counting and the orbit‐stabilizer theorem is utilized to verify the computation results.