Timeline for "Codes" in which a group of words are pairwise different at a certain position
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| S Jun 8, 2017 at 0:04 | history | suggested | Ryan Dougherty | CC BY-SA 3.0 |
Updated tables url
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| Jun 7, 2017 at 23:54 | review | Suggested edits | |||
| S Jun 8, 2017 at 0:04 | |||||
| Jun 20, 2014 at 16:40 | comment | added | Yuichiro Fujiwara | @HaoCHEN Thanks for the link! But I should have studied Chinese seriously at school... Google's translation is way better than me. Ugh! | |
| Jun 20, 2014 at 16:35 | comment | added | Hao Chen | And ... it is not yet the upperbound. I think the upperbound is 15, 13 is the new lowerbound. I'll write to the author of phftables.com, so that he can update it. | |
| Jun 20, 2014 at 16:35 | comment | added | Hao Chen | Actually, it is asked on a chinese forum. The problem is just replace "four" by "six". The posts are in chinese, but the second page contains the program. | |
| Jun 20, 2014 at 16:33 | comment | added | Hao Chen | Here is the link bbs.tianya.cn/post-71-144903-1.shtml | |
| Jun 20, 2014 at 16:32 | comment | added | Yuichiro Fujiwara | @Hao By the way, do you mind editing this post by giving a link/reference to the construction/search? If it was done by exhaustive search, $13$ must be the upper bound you asked, too. If you don't feel like it, you can just a link or reference as a comment; I'll edit this post when I have the time. | |
| Jun 20, 2014 at 16:22 | comment | added | Hao Chen | don't say that ... in that case mine also sucks ... | |
| Jun 20, 2014 at 16:20 | comment | added | Yuichiro Fujiwara | @HaoCHEN You mean PHF$(6;13,3,3)$, right? Thant's nice! I checked your 13 columns, too. It looks like a valid one, well, unless my programming sucks too hard! | |
| Jun 20, 2014 at 15:30 | comment | added | Hao Chen | In fact, I just saw a construction of (5;13,3,3), found by exhaustion (it seems), and I just checked it by program. Here it is: ['000000', '011111', '000112', '001120', '022210', '101200', '112022', '120111', '202101', '210200', '220221', '221011', '221202'] It is possible that I misunderstand something. | |
| Jun 20, 2014 at 15:26 | comment | added | Yuichiro Fujiwara | @HaoCHEN It is optimal in the sense that no PHF$(5;12,3,3)$ exists, i.e., you need at least $6$ rows to have $12$ columns with the all-distinct-symbol property. But I need to check the existing literature or prove it myself to see if it's optimal in your sense. I'm pretty sure it's the best among known PHF$(6;\vert C\vert,3,3)$, though. I'll edit my post if I find the answer to the optimality. Or you can prove it and improve this post, too! | |
| Jun 20, 2014 at 15:11 | comment | added | Hao Chen | By the way: This PHF(6;12,3,3), is it "optimal"? Is there a PHF(6;13,3,3)? | |
| Jun 20, 2014 at 15:10 | comment | added | Hao Chen | This answer is perfect for me. Thank you. | |
| Jun 20, 2014 at 15:01 | vote | accept | Hao Chen | ||
| Jun 20, 2014 at 14:57 | history | answered | Yuichiro Fujiwara | CC BY-SA 3.0 |