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In the book Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices by Wallis et al., Appendix A of the chapter on Hadamard matrices gives a list of known classes of Hadamard matrices. However, the list is a bit outdated since the book was published in 1972. Can anyone point me in the direction of a more up-to-date list of known orders for which a Hadamard exists? I've tried searching online but I haven't been able to find a large, diverse list like that given in the book by Wallis et al. Thanks in advance for any help.

Edit: In Appendix A of the book mentioned above, it compiles a list of known classes of Hadamard matrices and gives a brief justification for the existence of each class. For example, a couple lines from the table are: (where $q \equiv 3 \pmod{4}$ is a prime power)
+----------+---------------------------------+
| Order$\,\,\,\,\,\,$ | Justification$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$|
+----------+---------------------------------+
| $2^t$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,$ | Sylvester Construction $\,\,\,\,\,\,\,\,\,\,\,\,\,\,$ |
| $q(q+1)$ | Williamson; Corollary 8.14 $\,\,\,\,\,\,$|
+----------+---------------------------------+

I'm looking for a more up-to-date list that gives known classes similarly to this example

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There's a 1992 survey by J. Seberry and M. Yamada, "Hadmard matrices, sequences, and block designs", in Contemporary design theory: a collection of surveys, edited by J. H. Dinitz and D. R. Stinson that contains a table, "Orders of Known Hadamard Matrices". It lists orders by odd part, $q$, up to $q=2999$, and gives, for each $q$, the smallest $t$ for which a Hadamard matrix of order $q\cdot2^t$ is known as well as the construction method.

R. Craigen and H. Kharaghani have a chapter, "Hadamard matrices and Hadamard designs", in the Handbook of combinatorial designs, second edition (2007), edited by C. J. Colbourn and J. H. Dinitz, that gives a similar table up to $q=9999$, but without listing construction method.

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There is a large literature. Their order must be multiple of $4$ (or $1$ and $2$). In $2005$, Hadi Kharaghani and Behruz Tayfeh-Rezaie published their construction of a Hadamard matrix of order $428$. As a result, the smallest order for which no Hadamard matrix is presently known is $668$. As of $2008$, there are $13$ multiples of $4$ less than or equal to $2000$ for which no Hadamard matrix of that order is known, namely : $668, 716, 892, 1004, 1132, 1244, 1388, 1436, 1676, 1772, 1916, 1948$, and $1964$.

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  • $\begingroup$ Thanks for your comment, I appreciate the help. However, I think I worded my original question poorly. I've edited my question to (hopefully) explain more clearly the type of list I'm looking for. Do you happen to have any references to a list like that described in my edit? $\endgroup$ – Gecko Apr 8 '16 at 19:43
  • $\begingroup$ Reference: Hadamard matrix. $\endgroup$ – Will Orrick Apr 26 '16 at 12:07

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