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A search for the decay $B^0 \rightarrow φφ$ is made using $pp$ collision data collected with the LHCb detector at centre-of-mass energies of 7, 8 and 13 TeV, corresponding to an integrated luminosity of $9$ fb$^{-1}$. No significant signal is observed, and an upper limit on the branching fraction of $1.3~(1.4)\times 10^{-8}$ at $90 ~(95) \%$ confidence level is set. This result supersedes the previous LHCb study and improves the upper limit by a factor of two.