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In this paper we found the multiplicity distribution of the produced gluonsin deep inelastic scattering at large $z=\ln\LbQ^2_s/Q^2\Rb\,\,\gg\,\,1$ where$ Q_s $ is the saturation momentum and $Q^2$ is the photon virtuality. It turnsout that this distribution at large $n > \bar{n}$ almost reproduces the KNOscaling behaviour with the average number of gluons $ \bar{n} \propto \exp\Lbz^2/2 \kappa\Rb$, where $\kappa = 4.88 $ in the leading order of perturbativeQCD. TheKNO function $\Psi\Lb \frac{n}{\bar{n}}\Rb = \exp\Lb -\,n/\bar{n}\Rb$.For $n < \bar{n}$ we found that $\sigma_n \propto\Big( z - \sqrt{2\,\kappa\,\ln (n-1)}\Big)/(n-1)$. Such small $n$ determine the value of entropyof produced gluons $S_E = 0.3\, z^2/(2\,\kappa)$ at large $z$. The factor $0.3$stems from the non-perturbative corrections that provide the correct behaviourof the saturation momentum at large $b$.

Multiplicity distribution and entropy of produced gluons in deep inelastic scattering at high energies