On the exact value of Jung constants of Orlicz sequence spaces

The main result of this paper is: $JC(\ell^{(\Phi)}) = JC(\ell^\Phi) = 2^{1/C^0_\Phi-1}$ under some condition, where $JC(\ell^{(\Phi)})$, $JC(\ell^\Phi)$ are Jung constants of Orlicz sequence space $\ell^\Phi$ equipped with Luxemburg and Orlicz norm, respectively.