Construction of Structurally Incomplete Row-Column Designs with Pairwise Balance and/or Variance Balance Property

In this paper, construction methods of Structurally Incomplete Row-Column (SIRC) designs and a specific subset within this category called Balanced Incomplete Latin Square (BILS) designs (The treatments, rows, and columns all have an equal number), which satisfy the property of Pairwise balance (PB) and /or Variance Balance (VB) are presented. PB and/or VB SIRC/ BILS designs have been derived by employing symmetric BIB designs, combining two VB SIRC/BILS designs, and introducing treatments into pre-existing VB SIRC designs. For a ready reckoner, the catalogue of PB and/or VB SIRC/BILS designs that are obtainable from methods of construction for v (total treatments count), b1 (total rows count), b2 (total columns count), k1 (total count of non-empty nodes in rows) and k2 (total count of non-empty nodes in columns) have been prepared for v, b1, b2, k1, k2 .. 15.. KEYWORDS :Structurally incomplete row-column designs, Balanced Incomplete Latin Square designs, Pairwise balance, Variance balance.