#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 vdelecroix):
Replying to [comment:29 brett]:
> 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
Yes. It is possible to have that in #16227: we can replace the two
functions with one. But I am not sure it would be faster/clearer.
> - (anticipating ticket #16231) the OA/TD/MOLS object should have a
single internal format and then constructor operations to output other
equivalent objects. I think OA is the most general since it can have
arbitrary $t$ (Which TD does not) and arbitrary $\lambda$ (which MOLS
cannot have), etc. I think all internal operations should be done on OAs;
that is all constructions are as OAs. Then the object should be able to
output a TD or MOLS as alternatives. The user should be able to call for
whichever object they want but this would be just a case now of doing a
sanity check (make sure $t=2$ of they asked for TD), translate the
parameters to OA parameters, find the object if possible, and translate it
into the desired output format. This single internal format would
eliminate the possibility of methods eventually trying to call themselves
again. But the users will get the experience they expect with each type
of object.
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.
> - There are number of known parameters which cannot exist. The Bruck
Ryser Chowla Theorm gives the non-existence of many TD(n+1,n).
Additionally C. Lam proved that TD(11,10) cannot exist. Finally there is
some work that shows that if $k$ is large enough then the existence of
TD$(k,n)$ implies the existence of TD$(n+1,n)$ and so the non-existence
results can percolate downwards in $k$. I do not think we should have all
of the known results in this change. We should only implement the easy
ones or possibly none at all at first
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.
--
Ticket URL: <http://trac.sagemath.org/ticket/15310#comment:30>
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