Four Turyn type sequences of lengths 36, 36, 36, 35 are found by a computer search. These sequences give new base sequences of lengths 71, 71, 36, 36 and are used to generate a number of new T-sequences. The first order of many new Hadamard matrices constructible using these new T-sequences is 428.
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Kharaghani et al. (2004) studied this question.