#16272: redesign transversal designs
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Reporter: vdelecroix | Owner: Vincent
Type: enhancement | Delecroix
Priority: major | Status: new
Component: PLEASE CHANGE | Milestone: sage-6.2
Keywords: designs, orthogona arrays | Resolution:
Authors: Vincent Delecroix | Merged in:
Report Upstream: N/A | Reviewers:
Branch: | Work issues:
Dependencies: #15310, #16227 | Commit:
| Stopgaps:
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Comment (by brett):
In case "Unkown" did you mean that Sage does not know how to do it (as
currently implemented) but possibly Mathematics knows the answer?
"Unknown" should ideally mean that mathematics does not know the answer
but Sage development is likely to lag behind mathematics and I don't want
users to think that if Sage does not know the answer that this implies
that mathematics does not know the answer. I think this is all what you
meant but the word "nor" confused me.
The Bruck-Ryser-Chowla Theorem (from Theorem 2.13 in Stinson's Book) shows
that if $n \equiv 1,2 \bmod 4$
and there exists a prime $p \equiv 3 \bmod 4$ such that the largest power
of $p$ that divides $n$ is odd. Then a TD$(n+1,n)$ does not exist.
A reference for the non existence of TD$(11,10)$ is
@article {MR1018454,
AUTHOR = {Lam, C. W. H. and Thiel, L. and Swiercz, S.},
TITLE = {The nonexistence of finite projective planes of order
{$10$}},
JOURNAL = {Canad. J. Math.},
FJOURNAL = {Canadian Journal of Mathematics. Journal Canadien de
Math\'ematiques},
VOLUME = {41},
YEAR = {1989},
NUMBER = {6},
PAGES = {1117--1123},
ISSN = {0008-414X},
CODEN = {CJMAAB},
MRCLASS = {51E15 (51-04)},
MRNUMBER = {1018454 (90j:51008)},
MRREVIEWER = {J. C. Fisher},
DOI = {10.4153/CJM-1989-049-4},
}
For the results I mentioned about sufficiently high $k$ implying
TD$(n+1,n)$ exists, I will have to dig up the papers by Metz and review
them to remember exactly how this works.
--
Ticket URL: <http://trac.sagemath.org/ticket/16272#comment:4>
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