Storing (E-)optimal designs

[Leonard Soicher]

Dear All,

On Thu, Oct 14, 2004 at 03:50:00PM -0400, J P Morgan wrote:
> This in response to RAB's and LS's comments. I agree phi_1 is of interest. As 
> everyone may recall from 2003 discussions, I think lots of criteria are of 
> interest. It is the singling out of A as the orderer of choice that I don't 
> care for, especially in the multi-criteria framework we provide. On the one 
> hand, using it to order a list means nothing. On the other, it may imply some 
> implicit importance and/or ranking; requiring it seems do just that. 

Noted.

> We 
> provide the ability to rank by A (and other criteria) through the values we 
> store for those who so choose. Since we also have the efficiency values as 
> part of the external rep, which perform this function, ordering the list by 
> any chosen criterion seems a bit redundant.  But I can also see some value in 
> uniformity. Might ordering by a non-statistical criterion be a good 
> alternative? A possibility that neither uses nor implies anything about 
> statistical properties is to use the lex ordering of the designs themselves. 
> Certainly it could be implemented without reliance on any numerical algorithm 
> for eigenvalue extraction or other potential complications we discussed 
> extensively last Spring. This could be a suggested sort for a variety of 
> design lists regardless of their defining properties. This idea in some form 
> was also bandied about in Spring 2003.
> 

As I recall, we decided that as we were not requiring isomorphism
class representatives to be canonical in any way, there seemed
little to be gained by requiring lists of designs to be ordered
(length-first-lexicographically) by their lists of blocks.

I would also suggest that the external representation should drop 
its requirement that the designs in a list be distinct (the designs may
be coming through a pipe, produced by some heuristic search method).
Of course for our files database we require that designs in a list
be pairwise nonisomorphic.

All that said, I have programmed an "orderly generation" algorithm 
to compute, for a given (v,b,k), the lexicographically least 
isomorphism class representatives of the binary block designs with
that (v,b,k). I believe that I shall be able to generate all such designs
with v+b<=16, from which I can extract the best w.r.t.  whatever criteria
is of interest. I do not yet plan to put all the designs I generate onto
our web files database, since there are so many ( > 500,000 in one
of the lists ) and this might cause problems for our web server.

> LS's revised proposal for content indicators seems okay to me.
> 

Good. It's agreed then.

...

Regards,  Leonard