support the idea

[John P. Morgan]

On Date: Wed, 3 Sep 2003 15:31:43 -0600 Collin Carbno wrote

>
>I think the database of designs with statistical properties is a worthwhile
>activity.  How many designs are there to a  given size?  Any thoughts on
>range of designs to be cataloged.  Are we talking hundreds, thousands,
>millions, or billions of designs? What is your cutoff point?
>
> Good luck on the project.     Something that would be useful.
>_____________________

Thanks. The numbers will evolve as we progress. For v treatments in b blocks of 
size k our current thinking is all nonisomorphic designs in small cases. As v 
and/or b grow larger we will be drawing back from complete enumeration in ways 
not yet specified and certainly case dependent. From the statistical 
perspective, when not listing all designs, it is natural to restrict to those 
that behave reasonably well with respect to one or more of the optimality and/or 
robustness criteria (you might want to check the external representation 
document to see what is currently included in this regard). Obvious subclasses, 
like those of all regular graph designs for given (v,b,k), grow rapidly with v; 
there are values where it is reasonable to catalog, say, one design 
corresponding to each regular graph, but that number, too, rapidly becomes 
large. Equally strong arguments for inclusion of designs will be found in 
interesting properties purely from a combinatorial perspective. And a good bit 
of what is cataloged will depend on what people wish to contribute. Sorry this 
is so vague, but we can say there will be *many* designs.


J P Morgan
Department of Statistics
Virginia Tech