$C$ is a universal constant independent of both $N$ and $r$ . We show that such matrices are Bounded Orthonormal Systems (BOSs) with known upperbounds on their BOS constants . The new bounds provided herein on themaximum $ell^{\infty$-norms of their $\ell^2-normalized singular vectors allow for several previous Sigma-Delta quantization results to be generalized . Such finite difference matrices alsofundamental to standard$r^{\rm th}\$ order Sigma- Delta quantization schemesmore specifically, and as a result the new bounds provide herein on . themaximaximum . of their . normalized singular . norms allow for . several previous . Sigma- delta quantizationresults to be . improved and improved . In

Author(s) : Theodore Faust, Mark Iwen, Rayan Saab, Rongrong Wang