\begin{tikzpicture}[x=1cm,y=1cm,font=\small,>=Latex,
  every node/.style={text=black},
  constructive/.style={draw=blue!65!black,line width=1.2pt,-{Latex[length=2.0mm,width=1.45mm]}},
  probabilistic/.style={draw=orange!80!black,line width=1.2pt,-{Latex[length=2.0mm,width=1.45mm]}}]

\node[anchor=west] at (0,5.30) {length $L$};
\node at (6.10,5.30) {original vertices $n$};
\node[anchor=west] at (9.70,5.30) {construction};
\draw[->,black!65] (2.85,4.88)--(9.28,4.88);
\foreach \x/\lab in {3.05/3,4.80/9,6.55/210,8.30/222}{
  \draw[black!65] (\x,4.80)--(\x,4.96);
  \node[below=3pt] at (\x,4.80) {$\lab$};
}

\node[anchor=west] at (0,4.02) {$L=3$};
\draw[constructive] (3.05,4.02)--(9.28,4.02);
\fill[blue!65!black] (3.05,4.02) circle(2.0pt);
\node[anchor=west,align=left] at (9.70,4.02)
  {Quadratic matrix\\and certificates};

\node[anchor=west] at (0,3.03) {$L=4$};
\fill[black] (3.05,3.03) circle(2.0pt);
\draw[constructive] (6.55,3.03)--(9.28,3.03);
\fill[blue!65!black] (6.55,3.03) circle(2.0pt);
\node[anchor=west] at (9.70,3.03) {Symmetric profiles};

\node[anchor=west] at (0,2.04) {$5\le L\le11$};
\fill[black] (3.05,2.04) circle(2.0pt);
\draw[constructive] (8.30,2.04)--(9.28,2.04);
\fill[blue!65!black] (8.30,2.04) circle(2.0pt);
\node[anchor=west] at (9.70,2.04) {Four positions};

\node[anchor=west] at (0,.74) {$L\ge12$};
\draw[black!55] (2.50,1.25)--(2.38,1.25)--(2.38,.23)--(2.50,.23);
\fill[black] (3.05,.74) circle(2.0pt);
\draw[probabilistic] (4.80,1.10)--(9.28,1.10);
\fill[orange!80!black] (4.80,1.10) circle(2.0pt);
\node[anchor=west] at (9.70,1.10) {Probabilistic construction};
\draw[constructive] (8.30,.38)--(9.28,.38);
\fill[blue!65!black] (8.30,.38) circle(2.0pt);
\node[anchor=west] at (9.70,.38) {Four positions};

\node[anchor=west,font=\footnotesize] at (0,-.43)
  {Black dots at $n=3$: cycles. Arrows include every larger order.};
\node[anchor=west,font=\footnotesize] at (0,-.89)
  {Horizontal scale is categorical. Unmarked ranges receive no assertion here.};
\end{tikzpicture}