bibkey: brinkley2026incoherent authors: W. J. Brinkley, M. Fickus, J. Jasper and D. G. Mixon year: 2026 title: “Incoherent filter banks” doi: 10.48550/arXiv.2610.05302 url: https://arxiv.org/abs/2610.05302v1 claim: “We do not yet know whether a SUNTF_R(2, 5, 3) exists, and we leave this for future research.” strata_touched:

• D5/S3/QuantumBounds/Designs/StratifiedTightFrameTwoFiveThree license: citation-only triage: anchor

Incoherent filter banks

W. J. Brinkley, M. Fickus, J. Jasper and D. G. Mixon, Incoherent filter banks, arXiv:2610.05302v1 (2026).

Definition 3.2 (arXiv:2610.05302v1, Section 3, p. 8):

Let N and R be finite sets of cardinality N > 0 and R > 0, respectively. For each r ∈ R, let (φ_{r,n}){n∈N} be a finite sequence of unit vectors in a Euclidean space E_r over F. We say (φ{r,n}){n∈N, r∈R} is stratified if there exists Λ ≥ 0 such that (1/R) Σ{r∈R} |⟨φ_{r,n1}, φ_{r,n2}⟩|² = Λ for any distinct n1, n2 ∈ N. If this holds and each layer (φ_{r,n}){n∈N} is a UNTF for E_r where there exists D > 0 such that dim(E_r) = D for any r ∈ R, we call (φ{r,n}){n∈N, r∈R} a SUNTF for (E_r){r∈R} or a SUNTF_F(D, N, R).

The paper permits repeated vectors within a layer; its own SUNTF_R(2,5,5) in Example 4.4 repeats vectors.

Example 4.4 (last paragraph):

We do not yet know whether a SUNTF_R(2, 5, 3) exists, and we leave this for future research.

Locator

Author text: https://arxiv.org/abs/2610.05302v1.

• arXiv v1, Definition 3.2, Section 3, p. 8.
• arXiv v1, Example 4.4, last paragraph.
• DOI: https://doi.org/10.48550/arXiv.2610.05302