\documentclass{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{dateplot}
\usepgfplotslibrary{units}
\usepackage{siunitx}
\usepackage{tikz}
\usepackage{pgfplotstable}
\usepackage[utf8]{inputenc}
\pgfplotsset{/pgf/number format/use comma}

\begin{document}
\pgfplotstableread{
0 0.16
4 269.55
8 222.32
16 271.71
32 222.10
64 289.93
128 291.06
256 289.65
512 293.38
1024 349.66
2048 321.04
4096 488.41
8192 587.40
16384 2010.40
32768 2396.95
65536 3498.13
}\imballtoall

\begin{tikzpicture}
    \begin{axis}[
    	xmin=1,
    	xmax=65536,
    	xmode=log,
        ymin=0,
    	log basis x=2,
        xlabel={Nachrichtengröße [MiB]},
        ylabel={Zugriffszeit [ms]},
        width=15cm, height=10cm,
        change y base=true,
        y SI prefix=kilo
    ]
    	\addplot[smooth,blue] table {\imballtoall};
    \end{axis}
\end{tikzpicture}
\end{document}