Nonresolvable Incomplete Block Designs with Few Replicates

Abstract

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Construction of Optimal Block Designs by Computer

“…Of the 188 (v, k, r) combinations of Hall and Jarrett (1981) with 10 5 'u I 60, 2 I r < k 5 10, and r I 5, I could construct 93 RGD's, but these authors produced 95 RGD's. The three combinations for which I failed to find RGD solutions are (50,8,4), (52, 8, 4), and (54, 8, 4).…”

“…As such, my algorithm is more useful in situations in which there is no cyclic solution or there are more efficient noncyclic solutions. For example, the E of the cyclic solutions of the three combinations (12, 3, 6), (14, 3, 6), and (14, 5, 10) in table 3 of Hall and Jarrett (1981) are .7133, .7044, and .8601. These solutions are not RGD's.…”

Experimental Design: Review and Comment

“…Results on the Eoptimality of some balanced and partially balanced incomplete block designs were also given by Constantine (1981Constantine ( ,1982. Hall and Jarrett (1981) gave tables of incomplete block designs for experiments with many treatments (10 I u I 60) but no more than 5 replicates per treatment and block sizes of at most 10. John (1978) described a new balanced incomplete block design for u = 18 treatments in b = 51 blocks, with six runs per block and 17 replicates of each treatment.…”