@article{3065764, title = "On base and turyn sequences", author = "Koukouvinos, C. and Kounias, S. and Sotirakoglou, K.", journal = "Mathematics of Computation", year = "1990", volume = "55", number = "192", pages = "825-837", issn = "0025-5718, 1088-6842", doi = "10.1090/S0025-5718-1990-1023764-7", abstract = "Base sequences of lengths n + 1, n + 1, n, n are constructed for all decompositions of 4/1 + 2 into four squares for n = 19,., 24. The construction is achieved through an algorithm which is also presented. It is proved through an exhaustive search that Turyn sequences do not exist for n = 18,., 27; since Turyn sequences cannot exist for n = 28 or 29, the first unsettled case is n = 30. © 1990 American Mathematical Society." }