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While Tiet\\\"av\\\"ainen's bound was later improved for large values of $d$, it is still the best known upper bound for small values including the $d = o(n)$ regime. Tiet\\\"av\\\"ainen's bound holds also for $(d-1)$-wise independent probability distributions on $\\{0,1\\}^n$, of which linear codes with dual distance $d$ are special cases. 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