#15310: Wilson's construction of Transversal Designs/Orthogonal Arrays/MOLS
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Reporter: | Owner:
ncohen | Status: needs_review
Type: | Milestone: sage-6.2
enhancement | Resolution:
Priority: major | Merged in:
Component: | Reviewers:
combinatorics | Work issues:
Keywords: | Commit:
Authors: | d74341411288315f13da3d4383e515b884ba7440
Nathann Cohen | Stopgaps:
Report Upstream: N/A |
Branch: |
u/ncohen/15310 |
Dependencies: |
#15287, #15431 |
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Comment (by ncohen):
Yo !
> > With regards to the product construction, I think that when Wilson's
construction is passed $u=0$ then it should not check that TD$(k+1,t)$,
TD$(k,u)$, TD$(k,m+1)$ exist at all. It should check that TD(k,t)$ and
$TD(k,m)$ exist and call the product construction. Then in your
find_wilson_decomposition you should also include $u=0$ in the search
loops
I implemented it this way because I followed Douglas Stinson's book, which
defines this construction explicitly for 1<=u.
> This is an important issue I started to discuss with Nathann in
#15431... and I am in favour of implementing all the code with OA
conventions.
I hate useless abstraction. Look, for the moment there is some code left
in the constructor of MOLS but it will be removed soon, by the TD
construction. I am against forcing .... myself .... to translate every
construction of MOLS/TD into OA, because implementing code like that is
extremely tricky. I just spent two full days (no joke) because I
misunderstood one line of a construction, and I was helped by the guy who
actually first wrote it. I implemented code like #14562 and you wouldn't
believe the number of times I was convinced that the construction was
wrong. Look at the code, really. There is one line among those at which I
stared for 30 solid minutes. Only this line, nothing else. That's no joke,
and having to translate constructions from unclear papers can mean a lot
of headaches while you debug.
Anyway, right now I don't think that it is really a problem... There is a
lot of work needing to be done, and this work is implementing
constructions, any kind of constructions, in any formalism you like. We
can merge everything later if we need. But really what we need right now
are constructions, and nothing else.
> Cool: look at ticket #16272. I will add those references to the
description. If you have other non-existence theorems please post them on
#16272.
Yep, non-existence results are good and the Unknown truth value really
helps here. We could also implement something funny : if a guy ever needs
to say in a paper that "this design exists", we could have Sage return
some information on the path used by the constructions.
I mean. We can say where the basic constructions come from (we have the
references), and we can also say how the recursive constructions are
applied. Sooooo what we have is a way to say that this design can be
obtained by applying this or that constructions in this way,using the
following elementary blocks whose existence has been proved there and
there. Really, we can do that `:-)`
But that's nice things for later. What we need to do is beat the
Handbook's MOLS table while providing the actual MOLS. That would be
something we could boast about `:-P`
Nathann
--
Ticket URL: <http://trac.sagemath.org/ticket/15310#comment:31>
Sage <http://www.sagemath.org>
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