Higher order Hadamard matrices defined by recursive embedding:

- Since
does not exist, the FDN example figure above can be
redrawn for
, say, (instead of
), so that we can set
- The
*Hadamard conjecture*posits the existence of Hadamard matrices of order for all positive integers . - ``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. They are: 668,
716, 892, 1004, 1132, 1244, 1388, 1436, 1676, 1772, 1916, 1948,
1964.''
[
`http://en.wikipedia.org/wiki/Hadamard_matrix`]

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