#16662: OA for n=1046,1059,2164,3992,3994
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Reporter: ncohen | Owner:
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-6.4
Component: combinatorial | Resolution:
designs | Merged in:
Keywords: | Reviewers:
Authors: Nathann Cohen | Work issues:
Report Upstream: N/A | Commit:
Branch: u/ncohen/16662 | 2f936c57507cbd475f860a76b94ed44882d7de7b
Dependencies: #16604 | Stopgaps:
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Changes (by vdelecroix):
* status: needs_review => needs_info
Comment:
Hello,
Replying to [comment:30 ncohen]:
> 3) I am thinking of a data structure that would be useful to us, and
whose purpose is to store things like "all n such that there exists a
OA(k,n)" or even "all m such that there exists a OA(k,m), OA(k,m+1),
OA(k,m+2)".
+1
> What it stores: a set of integers defined by a boolean function
> What it is meant to answer: give the list of integers between x and y
such that the boolean function is satisfied.
>
> Of course we want to minimize the number of boolean function queries.
Even though it takes spaces, I am thinking of something like that:
>
> An array which associates to (any) integer n:
>
> a) if f(n) is computed: the smallest integer n'>=n such that f(n') is
True or has not been computed yet.
>
> b) if f(n) is not computed yet: None
>
> [...]
>
> This may be cool if we ever implement the `all_n` or `range_n` function.
And:
- what is the next value (like next_prime)
- what is the previous value (like previous_prime)
The problem with your approach is that you store a lot of data. It is
perhaps not as bad as what I imagine.
Questions:
1) why do you stop `n` at `N-3` in the first loop? I think that `n=N-1,
m=1, a=1, b=0, c=0` is a valid input:
{{{
sage: OA = thwart_lemma_3_5(3,13,1,1,0,0)
sage: is_orthogonal_array(OA,3,14,2)
True
}}}
So the bound should be `N-1`. Perhaps the particular case of `m=1` is
taken care by another construction, in that case, this must be documented
(and the upper bound for n updated accordingly).
2) the check `d <= n` is not necessary because of the lower bound on `c`.
I edit my commit at `u/vdelecroix/16662` to simplify the code with respect
to 2). As soon as 1) is solve, I would be happy to set this to positive
review.
Vincent
--
Ticket URL: <http://trac.sagemath.org/ticket/16662#comment:32>
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