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We survey the existence of base sequences, that is, four sequences of lengths \(m+p, m+p, m, m, p\) odd with zero auto-correlation function, which can be used with Yang numbers and four disjoint complementary sequences (and matrices) with zero non-periodic (periodic) auto-correlation function to form longer sequences. We survey their application to make orthogonal designs \(OD(4t; t, t, t, t)\). We give the method of construction of \(OD(4t; t, t, t, t)\) for \(t = 1, 3, \ldots, 41, 45, \ldots, 65, 67\), \(69, 75, 77, 81, 85, 87, 91, 93, 95, 99, 101, 105\), \(111, 115, 117, 119, 123, 125, 129, 133, 141, \ldots, 147, 153\), \(155, 159, 161, 165, 169, 171, 175, 177, 183, 185, 189, 195, 201, 203, 205, 209\).