The Trade Off Method in the Construction of BIB Designs with Variable Support Sizes.
ILLINOIS UNIV AT CHICAGO CIRCLE DEPT OF MATHEMATICS
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A balanced incomplete block BIB design with b blocks is said to have the support size b when exactly b of the b blocks are distinct. BIB designs with b b have interesting applications in design of experiments and controlled sampling. A method called trade off is introduced for the construction of BIB designs with repeated blocks. This method is utilized to study BIB designs with arbitrary v treatments is blocks of size k 3 in general and with v 7 and k 3 in particular. It is shown that BIB designs with v 7, k 3, and b, and any b exist if and only if b is divisible by 7 7 or b or min b,35 b not equal 8, 9, 10, 12, or 16 b,b not equal 28,24, 28,27, 35,30, 35,32, 35,33, 35,34, or 42,34.
- Statistics and Probability
- Operations Research