Results of search for Latin Squares


Advanced search

Message boards : Science : Results of search for Latin Squares

AuthorMessage
Martin
Send message
Joined: Dec 20 11
Posts: 1
Credit: 725,356
RAC: 0
Message 289 - Posted 2 Feb 2014 21:41:08 UTC

    Last modified: 2 Feb 2014 21:43:34 UTC

    Hi all,

    it looks like the search for Latin Square is now over.
    What was the result of the search?
    Was a valid triple of mutually orthogonal Latin squares of order 10 found?

    If not, was it possible to prove, that no
    triple of mutually orthogonal Latin squares of order 10 is possible?

    Or any other new information,
    which is helpful for mutually orthogonal latin squares in general?

    Or was the search just aborted,
    because problem took too long or was too difficult?

    Best regards,

    Martin

    Profile Oleg Zaikin [SAT@home]
    Forum moderator
    Project administrator
    Project developer
    Project scientist
    Send message
    Joined: Sep 15 11
    Posts: 133
    Credit: 4,826,453
    RAC: 0
    Message 291 - Posted 10 Feb 2014 9:23:36 UTC - in response to Message 289.

      Last modified: 28 Mar 2014 16:12:51 UTC

      Hi all,

      it looks like the search for Latin Square is now over.
      What was the result of the search?
      Was a valid triple of mutually orthogonal Latin squares of order 10 found?

      If not, was it possible to prove, that no
      triple of mutually orthogonal Latin squares of order 10 is possible?

      Or any other new information,
      which is helpful for mutually orthogonal latin squares in general?

      Or was the search just aborted,
      because problem took too long or was too difficult?


      For this experiment we used the following strategy. We started from aproximation of the triple - 1st square is orthogonal to 2nd and 3rd squares, 2nd and 3rd squares were not orthogonal at all. After it we tried to find triples with 50 orthogonal cells between 2nd and 3rd squares, then for 60 and so on. Finaly in the best triple we found 2nd and 3rd squares were orthogonal in 71 cells (from 100). In fact we failed to find something better and because of it this experiment was aborted.
      We will try to find triple of MOLS of order 10 by another approach.
      We will start from currently best approximation of such triple, it was found
      by prof. Wanles. In this triple 1st square is orthogonal to 2nd and 3rd squares,
      2nd and 3rd squares are partly orthogonal - they has 91 different cells combinations from 100 needed. We will use local search strategy to find better approximation. This experiment will be started in March, I hope so. Right now I prepare experiment aimed to solve hard cryptanalysis problems for Bibium cipher.
      This problem partly discussed in our arxiv paper.

      Post to thread

      Message boards : Science : Results of search for Latin Squares


      Home | My Account | Message Boards


      Copyright © 2019 Institute for System Dynamics and Control Theory of SB RAS and Institute for Information Transmission Problems of RAS