11 problems

Let $d$ be the dimension of a real symplectic vector space, and let a $d\times n$ ETF denote an equiangular tight frame in that space. Symplectic Zauner's conjecture. There exists…

Let $d>3$. An equiangular tight frame (ETF) with parameters $(r,n)$ is a set of $n$ unit vectors in $\mathbb{S}^{r-1}$ whose coherence attains the Welch bound. XXY's ETF existence…

Paley ETF spark and bender conjecture. The spark of $\Phi_q$ is $((p+1)/2)^s$ and the bender is a $(p^s, ((p+1)/2)^s,\lambda)$-BIBD.

$4\times8$ uniqueness conjecture. There exists a unique complex $4\times8$ ETF up to switching equivalence.

Weak $d\times 2d$ conjecture. For every $d$, there exists a $d\times 2d$ ETF.

Let $d\geq 5$. An equiangular tight frame (ETF) with parameters $(d,n)$ is a real ETF for $\mathbb{R}^d$ of size $n$. ETF extension conjecture. There exists an ETF with parameters…

Binder BIBD conjecture. The binder of $\mathcal G(p,\ldots,p)$ is a

Let $D$ and $N$ be positive integers with $N>2D>2$, and let a real $\operatorname{ETF}(D,N)$ denote a real equiangular tight frame of $N$ vectors in dimension $D$. Call $(D,N)$ pos…

Let $D$ and $N$ be positive integers with $N>2D>2$, and let an $\operatorname{ETF}(D,N)$ denote a complex equiangular tight frame of $N$ vectors in dimension $D$. Call $(D,N)$ posi…

Mixon's divisibility conjecture. There exists an $n$-vector equiangular tight frame in $\mathbb{C}^d$ only if one of these quantities divides the product of the other two.

Let $M\geq 2$. An equiangular tight frame (ETF) in $\mathbb{C}^M$ with $N$ vectors is denoted by $\operatorname{ETF}(M,N)$; the maximal possible number of vectors in the complex ca…