Construction of efficiency balanced block designs through reinforcement

This paper gives some new construction methods of Efficiency Balanced block designs through reinforcement of new treatment(s) to the blocks (may not be to all the blocks) of a given Balanced Incomplete Block (BIB) design. The first construction method provides an Efficiency Balanced design with the number of treatments v+1, starting from a BIB design with the number of treatments v and the second one provides an Efficiency Balanced design with the number of treatments v₁+v₂, starting from two Balanced Incomplete Block designs with the number of treatments v_i (i=1,2). An example of the first construction method shows that the efficiency factor of the resulting Efficiency Balanced design is greater than that of the parent Efficiency Balanced (i.e., BIB) design.