“…The extended SSD d $ is represented as an (n+r)  m matrix X $ ½X 0^A0 0 , where A is an r  m matrix with entries71 of the additional r runs. X $ attains the new lower bound to E(s 2 ), given in Theorems 2.1 and 2.2, when (i) A is an E(s 2 )-optimal SSD(r, m) using the bounds given by Das et al (2008) or Suen and Das (2010), depending upon whether r is even or odd, respectively, and (ii) AX 0 ¼ 0, for even m or AX 0 ¼ E for odd m, where 0 is a null matrix and E is a r  n matrix with entries 71.…”