We compute Polak's bound $A_4(19,6,8)$ for binary constant weight codes, obtaining the numerical value $673.04001$. An exact rational certificate gives $A_4(19,6,8)\le 673.0400143064802474039375132665301315202504$, and hence $A(19,6,8)\le 673$. This improves the upper bound $693$ listed in Brouwer's table. The certificate is verified by a separate program using exact rational arithmetic.

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