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I am interested in complete catalogs of non-isomorphic conference matrices, similar to those of Hadamard matrices. Do such catalogs exist? If yes, then where could they be found, and what is an accessible reference? If no catalogs exist, are there different construction methods?

Thank you in advance, Peter Goos KULeuven

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    $\begingroup$ Have you checked the Handbook of Combinatorial Designs? They might give as complete a catalog as you are likely to find off the web. Also, it is likely (but I do not know) that the number is super exponential in the order of the matrix, so it is not clear to me what you would do with a catalog. $\endgroup$
    – The Masked Avenger
    Commented Jun 17, 2015 at 16:10
  • $\begingroup$ I just checked the Handbook, and it lists a variety of constructions and some information about the spectrum of orders for which a conference matrix exists. However there is no mention of enumeration or cataloguing etc. So at least it might be useful for the constructions. $\endgroup$
    – Gordon Royle
    Commented Jun 18, 2015 at 2:30

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Here you have a catalog for conference matrices. Unfortunately it doesn't work but you can contact to the author. Maybe the webpage has been changed

http://www.math.ntua.gr/~ckoukouv/conference.htm

Best, Dardo

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