Asymmetric SICs over finite fields

Zauner’s conjecture concerns the existence of $d^2$ equiangular lines in ${\mathbb{C}}^d$; such a system of lines is known as a SIC. In this paper, we construct infinitely many new SICs over finite fields. While all previously known SICs exhibit Weyl–Heisenberg symmetry, some of our new SICs exhibit trivial automorphism groups. We conjecture that such $\mathit{\text{totally}}\mathit{\text{asymmetric}}$ SICs exist in infinitely many dimensions in the finite field setting.