On the E-Optimality of Some Block Designs

Summary This paper is concerned with the investigation of E-optimal block designs. Some conditions are given under which there is a regular graph design which is E-optimal. Immediate applications of these results demonstrate that a great majority of the designs obtained by John and Mitchell (1977) are indeed E-optimal. It can also be shown that a group-divisible design with λ1 = λ2 + 1 > 1 and group size 2 is E-optimal. The same result also holds for a PBIB design with a cyclic scheme, λ2 = λ1 ± 1, and v = 5. Another application shows that if d is a BIBD, a group-divisible design with λ2 = λ1 + 1, a group-divisible design with λ1 = λ2 + 1 > 1 and group size 2, or a PBIB design with a cyclic scheme, λ2 = λ1 ± 1 and v = 5, then the dual design of d is also E-optimal.