On the Type-1 Optimality of Nearly Balanced Incomplete Block Designs with Small Concurrence Range
نویسندگان
چکیده
The class of nearly balanced incomplete block designs with concurrence range l, or NBBD(l), is defined. This extends previous notions of “most balanced” designs to cover settings where off-diagonal entries of the concurrence matrix must differ by a positive integer l ≥ 2. Sufficient conditions are found for optimality of NBBD(2)’s under type-1 criteria, then used to establish Aand D-optimality in settings where optimal designs were previously unknown. Some NBBD(3)’s are also found to be uniquely Aand D-optimal. Included is a study of settings where the necessary conditions for balanced incomplete block designs are satisfied, but no balanced design exists.
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