OCDs in Balanced Incomplete Block Design Set-Up

In this chapter, we consider the problem of finding optimum designs for the estimation of covariate parameters in a BIBD with parameters $$v,~b,~r,~k,~\lambda $$ v , b , r , k , λ . When $$n\ne $$ n ≠ 0 (mod 4), it is not possible to find designs attaining minimum variance ( $$\frac{\sigma ^2}{n}$$ σ 2 n ) for the estimated covariate parameters. Conditions for D-optimum designs for the estimation of covariate parameters are established with the usual assumption that each of the values of the csovariates belongs to the interval [ $$-1,1$$ - 1 , 1 ]. Some constructions of D-optimal designs have been provided for symmetric balanced incomplete block design (SBIBD) with parameters $$b=v,~r=k=v-1,~\lambda =v-2$$ b = v , r = k = v - 1 , λ = v - 2 when $$k\equiv 2$$ k ≡ 2 (mod 4) and b is an odd integer.