On the Connectedness of A Set of Twenty-Three (23) Optimal Incomplete Block Designs of Size (T=9, B=9, K=3, R=3) Based on Circuits

In this article, six (6) Incomplete Block Designs (IBDs) namely; A, B, C, D, E and F of size due to Nguyen, (1994) were extended by the construction of additional seventeen (17) new IBDs namely; G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V and W using all the initial blocks in Nguyen’s via the cyclic method and JAVA codes. All the 23 IBDs were enumerated for “robustness” based on number of circuits; through shorter path-lengths. Our newly constructed design Q, turned out to be better than Nguyen’s designs A-F with 28 shorter paths which is closely followed by designs G, K, N, O, P, S, V and W with 27 shorter-paths each. Design Q turned out to have the least number (8) of longer paths which makes it the best design for experimentation in terms of circuits. Incidentally, Nguyen’s design A turns out to be the least connected design among all the 23 IBDs with only one longest path. In conclusion, we discovered that the overall best design is design Q based on connectedness. Therefore, design Q from the newly constructed designs becomes the most robust in terms of design connectedness and hence recommended for use with their experimental layouts to experimenters, investigators or evaluators who seek for the best optimal design of size in any field experiment.