A total Boolean function on 2,017,584 variables has block sensitivity at least λ^{2.127}, with λ the spectral sensitivity, so bs is not O(λ²).
Complexity measures and decision tree complexity: a survey,
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Block Sensitivity can exceed Spectral Sensitivity Squared
A total Boolean function on 2,017,584 variables has block sensitivity at least λ^{2.127}, with λ the spectral sensitivity, so bs is not O(λ²).