Hadamard matrices of small order and Yang conjecture

Abstract

We show that 138 odd values of n less than 10000 for which one knows how to construct a Hadamard matrix of order 4n have been overlooked in the recent handbook of combinatorial designs. There are four additional odd n, namely 191, 5767, 7081 and 8249, in that range for which we can construct a Hadamard matrix of order 4n. Our exhaustive computer searches show that the near-normal sequences NN(n) exist for n=36,38,40. Thus the Yang conjecture on the existence of NN(n) for all even n has been verified for n <= 40 but it still remains open.