#16391: Helper functions for OA constructions
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Reporter: ncohen | Owner:
Type: enhancement | Status: needs_info
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 ncohen):
Yo Vincent !
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.
And so what ? Do I throw all my useful code away because of that ? I
really have no other way to generate these designs.
> 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.
Nathann
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Ticket URL: <http://trac.sagemath.org/ticket/16391#comment:8>
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