Abstract
Let λ(m) denote the maximal absolute projection constant over real m-dimensional subspaces. This quantity is extremely hard to determine exactly, as testified by the fact that the only known value of λ(m) for m>1 is λ(2)=4/3. There is also numerical evidence indicating that λ(3)=(1+5)/2. In this paper, relying on a new construction of certain mutually unbiased equiangular tight frames, we show that λ(5)≥5(11+65)/59≈2.06919. This value coincides with the numerical estimation of λ(5) obtained by B. L. Chalmers, thus reinforcing the belief that this is the exact value of λ(5).
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