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Search for the population of the low-energy continuum of tetraneutron systemwas performed for the $^2$H($^8$He,$^6$Li)$^4n$ and$^2$H($^8$He,$^3$He)$^7$H$\rightarrow ^3$H+$^4n$ reactions. Evidence for a humpin the $^4n$ continuum at about 3.5 MeV was observed in both reactions. Theobserved statistics is quite low (6 and up to 40 events) corresponding to verylow cross sections of few microbarns or tens of microbarns. The backgroundconditions for the $^2$H($^8$He,$^6$Li)$^4n$ reaction are shown to be good,favoring the physical nature of the observed events. The$^2$H($^8$He,$^3$He)$^7$H$\rightarrow ^3$H+$^4n$ process transforms to the$^2$H($^8$He,$^6$Li$^{\ast})^4n$ reaction in the limit of the highest $^7$Hdecay energies. The population of the low-energy region in the $^{4}$n spectrumis found to be perfectly correlated with the population of the lowest $^{6}$Listates in the $^{3}$He+$^{3}$H continuum. Theoretical calculations of $^{8}$Hein a five-body $\alpha$+$4n$ and of $^{4}$n in a four-body hypersphericalmodels are presented. The $^{8}$He wave function is shown to contain strongspecific correlations, which may give rise to very low-energy structures intetraneutron continuum in extreme-peripheral reaction scenarios.

Population of tetraneutron continuum in reactions of $^{8}$He on deuterium