  An equiangular tight frame (ETF) is a set of equal norm vectors in a
Euclidean space whose coherence is as small as possible, equaling the Welch
bound. Also known as Welch-bound-equality sequences, such frames arise in
various applications, such as waveform design, quantum information theory,
compressed sensing and algebraic coding theory. ETFs seem to be rare, and only
a few methods of constructing them are known. In this paper, we present a new
infinite family of complex ETFs that arises from hyperovals in finite
projective planes. In particular, we give the first ever construction of a
complex ETF of 76 vectors in a space of dimension 19. Recently, a
computer-assisted approach was used to show that real ETFs of this size do not
exist, resolving a longstanding open problem in this field. Our construction is
a modification of a previously known technique for constructing ETFs from
balanced incomplete block designs.
