#16391: Helper functions for OA constructions
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Reporter: ncohen | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.3
Component: combinatorial | Resolution:
designs | Merged in:
Keywords: | Reviewers:
Authors: Nathann Cohen | Work issues:
Report Upstream: N/A | Commit:
Branch: u/ncohen/16391 | 2090875de8a5d9a0301a85fc35e0e60a068de1ab
Dependencies: #16370 | Stopgaps:
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Comment (by vdelecroix):
Hi Nathann,
Thanks for your clarification.
Replying to [comment:8 ncohen]:
> I cannot claim that `OA_with_holes` will always output "optimal
results", and I never did.
>
> I need those designs for constructions of OA that we cannot build at the
moment, and I have no other way to produce them. What is the problem with
seeing this function as
>
> 1) When k<=3 we know that it exists
> 2) When there is a `OA(k+1,n)` we know that it exists
> 3) If everything else fails, see if you are lucky
>
> And you want me to remove feature 3), even though it does return helpful
things. I never claimed that the results would not change, and what I know
for sure is that the results WILL improve as we add new OA. It is true, I
cannot prove that eventually feature 3) will never become less powerful.
I do not want you to remove it but I do not want to see code or doctests
that depend on the lucky case 3). Which implies that you should not use `k
> 3` anywhere. In the current ticket this function is not used at all,
so... Where this code is merged with #16391?
> > The multiplicity of TD(k,1) you obtain must strongly depend on the way
you did your construction
>
> We have no proof of that. And I did not claim the contrary, but we have
no proof of that. For instance the proof that it always exists when k<=3
is the proof that any OA contains an independent set of size 3, which
means that the result will always hold in this case regardless of which OA
is returned.
Is there a way to find the largest set of disjoint blocks?
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/16391#comment:10>
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