indicators

[R A Bailey]

Duals and optimality

> >
> >>From a statistician's perspective, some optimality results are known
> >for designs
> >>which are duals of BIBDs.
> >
> >We know more than this.  Given the numbers of treatments and blocks and
> >replications and block sizes, a binary block design is optimal iff its
> >dual is.
> >
> >RAB
> >
> 
> Yes, that's right in a certain sense: if we restrict to eigenvalue-based 
> criteria. It does not always hold for, say, the MV-criterion. Moreover, the 
> restriction to equal replication is, for many optimality workers, not part of 
> the most natural optimality framework, which is "determine the best design for 
> given v,b,k." Some results are known in this wider setting for duals of optimal 
> designs, but in many cases the general problem for the class (v,b,k) without 
> restriciting to equireplication remains open.
> 
> JP  
> 

Optimality of duals does not require equal replication.

RAB


-- 
R. A. Bailey
       
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