#16231: Equivalence between OA/TD/MOLS
-------------------------+-------------------------------------------------
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: | a46446f3b29690aa1245583639bb6b78b3d50dca
Nathann Cohen | Stopgaps:
Report Upstream: N/A |
Branch: |
u/ncohen/16231 |
Dependencies: |
#15310, #16227 |
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Comment (by vdelecroix):
Hello,
Remainder: the content of this ticket has been partially discussed in
#15310 and #16227.
I assume that the big goal of this ticket is also to find more
constructions.
The operation which consists in removing groups is trivial. So instead of
given a couple (k,n) look for a TD(k,n) it is just more meaningful for a
given n to have functions which:
- return the largest k such that Sage knows how to build a TD(k,n) and
provide it
- the smallest k such that Sage knows that there does not exist a TD(k,n)
and provide the Theorem that says so (see also #16272 for that)
Removing this feature from the MOLS in is '''very''' bad. I would rather
try to make it available in the other functions. Doing it by "trying all
`k` before it says no" does not look like a good strategy to me.
In order to find new TD(k,n), we have different strategies:
- ''individual constructions'' (currently there is `TD_6_12` and also the
ones introduced in #16241 #16236 and #16235)
- ''family constructions'' (these are currently included into
`orthogonal_array` and `mutually_orthogonal_latin_squares`). It is hard
for me to tell if those constructions overlap.
- ''generalized Wilson constructions'' which build TD(k,n) from "smaller"
ones
- ''translations'', which is basically what this ticket is about
Is that all? I would like this to be clear before thinking about what you
did.
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/16231#comment:3>
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