A Bit-Parallel Tabu Search Algorithm for Finding Es2-Optimal and Minimax-Optimal Supersaturated Designs

We prove the equivalence of two-symbol supersaturated designs (SSDs) with N (even) rows, m columns, and smax=4t+i, where i∈0,2 and t∈ℤ≥0 and resolvable incomplete block designs (RIBDs) whose any two blocks intersect in at most N+4t+i/4 points. Using this equivalence, we formulate the search for two-symbol Es2-optimal and minimax-optimal SSDs with smax∈2,4,6 as a search for RIBDs whose blocks intersect accordingly. This allows developing a bit-parallel tabu search (TS) algorithm. The TS algorithm found Es2-optimal and minimax-optimal SSDs achieving the sharpest known Es2 lower bound with smax∈2,4,6 of sizes N,m=16,25, (16, 26), (16, 27), (18, 23), (18, 24), (18, 25), (18, 26), (18, 27), (18, 28), (18, 29), (20, 21), (22, 22), (22, 23), (24, 24), and (24, 25). In each of these cases, no such SSD could previously be found.