id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
16272,redesign transversal designs,vdelecroix,Vincent Delecroix,"The tickets #15310 and #16227 introduce a nice `availability` keywords to the function `transversal_design`. With `availability=True` the return value is the answer to the question ""Does Sage know how to build a TD(k,n)""? Using `Unknown` from `sage.misc.unknown` we can turn the question into ""Do we know mathematically that a TD(k,n) exist?"" whose answer would be:
- `True` if Sage knows how to do it
- `Unknwon` if neither Sage nor mathematics can help
- `False` if we know mathematically that such construction does not exist
As the semantic changes, we will also turn the keyword `availability` into `existence` (or maybe have both).
In the same ticket, we will include some of the known non existence of transversal designs:
- The [http://en.wikipedia.org/wiki/Bruck%E2%80%93Ryser%E2%80%93Chowla_theorem Bruck Ryser Chowla Theorm] gives the non-existence of many TD(n+1,n)
- C. Lam in Lam, ""The Search for a Finite Projective Plane of Order 10"" (1991) proved that TD(11,10) cannot exist
And we might see later
- 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",enhancement,closed,major,sage-6.3,combinatorics,fixed,"designs, orthogona arrays",ncohen brett,,"Nathann Cohen, Vincent Delecroix","Nathann Cohen, Vincent Delecroix",N/A,,e2749b3db4cd78fc5e9ea8219d4cdf895b283465,e2749b3db4cd78fc5e9ea8219d4cdf895b283465,#16231,