Timeline for Packings with block size equal to $6$?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jan 3, 2020 at 0:01 | comment | added | Elaqqad | I have discovered some new information, but I did not understand the construction, I did not quite get how to "add six 6-lines in the groups" if somebody can help? | |
| Jan 3, 2020 at 0:01 | history | edited | Elaqqad | CC BY-SA 4.0 |
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| Jan 2, 2020 at 18:48 | comment | added | Elaqqad | @ Max Alekseyev, thanks for the article. I will read it and see if I can use the same algorithm for packings. | |
| Jan 2, 2020 at 18:47 | comment | added | Elaqqad | @KenW.Smith, I already checked the book thanks. Yeah, there are a lot of articles focused on the case $k=5$. But, I was asking if there is some new advances since the publication of the book (as today we have more computer power than years ago). Otherwise, as you said, it should still be open. | |
| Jan 2, 2020 at 12:48 | comment | added | Max Alekseyev | Perhaps, Gerhard means this article arxiv.org/abs/math/9502238 | |
| Jan 2, 2020 at 3:49 | comment | added | Ken W. Smith | The CRC Handbook of Combinatorial Designs, 2nd ed., (2007) has seven pages on packings. Skimming through those pages (email me for a copy) says almost nothing about $k=6$ and I know a lot of work went into $k=5$, so I suspect your question is pretty open? The CRC section does reference an old survey by W. H. Mills and R. C. Mullin, "Coverings and Packings" in Contemporary Design Theory, Wiley, 1992. | |
| Jan 2, 2020 at 1:22 | comment | added | Gerhard Paseman | The website has been rearranged. The older version had a link to a paper by many authors (I believe Greg Kuperberg was one), and my sometimes faulty memory tells me that packing was related to covering in that paper (this may be a wrong assertion). At this point, you should wait awhile until someone with a better memory responds here, and then contact Dan Gordon if you don't get satisfaction here. Gerhard "Sorry To Raise Hope Prematurely" Paseman, 2020.01.01. | |
| Jan 2, 2020 at 1:07 | comment | added | Elaqqad | @Gerhard, it took me time, but I did not manage to find your article on la Jolla Repository, do you have a link ? Thank you ! | |
| Jan 2, 2020 at 0:21 | comment | added | Elaqqad | I think that taking the complement of a each block in a packing produces another packing (the same goes for coverings) . Their sizes are very close. but different. we have $D(v,k)\leq f(k,v)\leq C(v,k)$ for some known function $f$. where $C(v,k)$ is the minimal size of a covering | |
| Jan 2, 2020 at 0:05 | comment | added | Gerhard Paseman | There should be some tight relation between packing and coverings. Something like a packing for n, k leads by complementation to a covering for n,n-k. Check out Handbook of Combinatorial Designs. Also check out La Jolla repository. Gerhard "Little Fuzzy On Packing Thinking" Paseman, 2020.01.01. | |
| Jan 1, 2020 at 23:57 | history | asked | Elaqqad | CC BY-SA 4.0 |