Existence of cyclic 2-designs in an infinite family of dimensions

A cyclic 2-design is a finite unitary orbit whose associated decohered probability vectors form a simplex 2-design. Infinite-family conjecture. Cyclic 2-designs exist in an infinite family of dimensions. An explicit theorem immediately preceding the conjecture proves existence in an infinite family using robust Hadamard matrices and difference sets, while the source labels the broader numerical extension as conjectural; the precise intended distinction should be checked.