A construction is given of 2 9 (d+1)² equiangular lines in Euclidean d-space, when d = 3 · 2²ᵗ⁻¹-1 with t any positive integer. This compares with the well known "absolute" upper bound of 1 2 d(d+1) lines in any equiangular set; it is the first known constructive lower bound of order d² .
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D. de Caen (2000) studied this question.