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Nov 2, 2017 at 22:47 history edited kodlu CC BY-SA 3.0
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Nov 2, 2017 at 22:03 comment added Gerhard Paseman @Noam, except I disagree with this evaluation of most also. My metric for odd k is t, the power of 2 for which we know a matrix of order k2^t exists. The reference posted by Orrick above is recent. When I find something more recent (or understand the effectiveness of Keevash's recent work), I will post more. Gerhard "Progress Can Be A Function" Paseman, 2017.11.02.
Nov 2, 2017 at 20:40 comment added Noam D. Elkies You might also note that for most large k we do not know how to construct a Hadamard matrix of order 4k; the fact that the smallest open case is 167 is misleading. The density of k for which we know a Hadamard matrix decays as c/log(k); for example, one construction assumes 4k-1 is prime.
Nov 2, 2017 at 20:04 history answered Gerhard Paseman CC BY-SA 3.0