A class of BIB designs with repeated blocks

Balanced incomplete block design (BIBD) with repeated blocks is studied in detail. Methods of construction of BIB designs with repeated blocks are developed so as to distinguish the usual BIBD and BIBD with repeated blocks. One additional parameter, say d, is considered here, where d denotes the number of distinct blocks present in the BIB design with repeated blocks. Further, a class of BIB design with parameters: v = 7, b = 28, r = 12, k = 3, u = 4, has been constructed where, out of 15, 14 BIB designs have repeated blocks. These 15 BIB designs, which have the same parameters, are compared on the basis of number of distinct blocks (d) and the multiplicities of variance of elementary contrasts of the block effect.