All of you will be relieved to know there is an alternative hypothesis on the supply of Hadamard matrices. If we are willing to admit transient behavior at low orders, then the entropy of Hadamard matrices shows scaling behavior when we allow for it to grow as N^phi for an exponent phi less than 2. Again, using available data up to N = 32, a value of phi between 1.4 and 1.8 seems to be singled out. Here’s what I get for phi=1.6: N log_2(num(N)) / N^phi 4 1.04302 8 1.15610 12 1.20338 16 1.25669 20 1.25455 24 1.27412 28 1.25239 32 1.25612 There’s a strong transient up to N=12. What’s slightly remarkable is how the near convergence of the subsequent values strongly depends on phi. This hypothesis, should it be true, raises two points: (1) The exponent phi should be added to the list of “basic things about Hadamard matrices we have no clue about”. (2) Hadamard hunters may wish to cast a wider net. Almost all searches (such as for order N=668) have been for constructions based on sequences, that is, a much lower entropy source corresponding to phi=1. -Veit