The minimal 2-design conjecture

Let a 2-design in dimension $d$ be a finite projective 2-design, and let a SIC denote a symmetric informationally complete measurement while an MUB denotes a complete set of mutually unbiased bases. Minimal 2-design conjecture. Any 2-design in dimension $d$ with no more than $d(d+1)$ elements is either a SIC or MUB. The preceding discussion establishes the corresponding minimality and uniqueness result for Clifford-covariant 2-designs, but the assertion for arbitrary 2-designs is presented as a stronger conjectural statement.