A bit-parallel tabu search algorithm for finding E(s^2)-optimal and minimax-optimal supersaturated designs
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We prove the equivalence of two-symbol supersaturated designs (SSDs) with N (even) rows, m columns, s_ max = 4t +i, where i∈{0,2}, 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 E(s^2)-optimal and minimax-optimal SSDs with s_max∈{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 E(s^2)-optimal and minimax-optimal SSDs achieving the sharpest known E(s^2) lower bound with s_max∈{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.
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