Tight incomplete block designs

Optimal Incomplete Block Designs

Optimal incomplete block designs are pursued through the E-criterion of minimizing maximal variance. Methodology is developed for design choice based on graphs and an extensive catalog of downloadable designs compiled. Along with the general methodology, a near complete solution for E-optimal block designs is provided for up to 15 treatments. E-optimality is revealed as a flexible criterion tha...

Incomplete Block Designs

1. Introduction These designs were introduced by Yates in order to eliminate heterogeneity to a greater extent than is possible with randomized blocks and Latin squares when the number of treatments is large. The precision of the estimate of a treatment effect depends on the number of replications of the treatment-the larger the number of replications, the more is the precision. Similar is the ...

Splitting balanced incomplete block designs

Beautifully Ordered Balanced Incomplete Block Designs

Beautifully Ordered Balanced Incomplete Block Designs, BOBIBD(v, k, λ, k1, λ1), are defined and the proof is given to show that necessary conditions are sufficient for the existence of BOBIBD with block size k=3 and k1=2 and for k=4 and k1=2 except possibly for eleven exceptions. Existence of BOBIBDs with block size k=4 and k1=3 is demonstrated for all but one infinite family and the non-existe...

Remarks on Balanced Incomplete Block Designs

Proof. Assume the hypothesis and the falsity of either conclusion. Construct matrix A of 2x + 2 rows and 4x+4 columns, with entries + 1 and — 1. The first column contains exclusively +1, and the second column — 1. Set up one-to-one correspondences between rows of A and elements of D ; between columns other than the first two of A and blocks of D. Enter +1 if the element is contained in the bloc...