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We present a method for constructing two-level supersaturated designs (SSDs) from incomplete block designs. A lower bound of E(s 2 ) that also covers the case of odd run sizes is given. This bound is attained by SSDs constructed from balanced incomplete block designs. We study SSDs that can be constructed from regular graph designs when balanced incomplete block designs do not exist. A computer search is conducted to find SSDs with 5 ≤ n ≤ 50 and n ≤ m ≤ 2n that can be constructed from regulardoi:10.1198/004017007000000452 fatcat:b2v6lsxepzg33goxp3ubdxk5eu