Every (n-2)-dimensional subspace of R^n (n even) contains a nonzero vector with largest-to-second-largest absolute entry ratio at least n/2 - 1, and the general lower bound on single-error detection height is tight when n-k divides k.
Analog error-correcting codes
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Tight Lower Bounds on The Single-Error Detection Threshold for Analog Error-Correcting Codes
Every (n-2)-dimensional subspace of R^n (n even) contains a nonzero vector with largest-to-second-largest absolute entry ratio at least n/2 - 1, and the general lower bound on single-error detection height is tight when n-k divides k.