\documentclass{standalone}
\usepackage{cartonaugh}
\begin{document}
  % draw cell implicants(single, horizontal, vertical, and 2x2 block), default submap
  \begin{cartonaugh}[2][2][1]
    % single cell
    \implicant{0}{0}
    % horizontal
    \implicant{2}{3}
    % vertical
    \implicant{1}{3}
    % block
    \implicant{0}{3}
  \end{cartonaugh}
  \begin{cartonaugh}[2][4][1]
    % single cell
    \implicant{0}{0}
    \implicant{1}{1}
    % horizontal
    \implicant{2}{3}
    % vertical
    \implicant{3}{7}
    % block
    \implicant{6}{5}
  \end{cartonaugh}
  \begin{cartonaugh}[4][2][1]
    % single cell
    \implicant{0}{0}
    \implicant{1}{1}
    % horizontal
    \implicant{4}{5}
    % vertical
    \implicant{1}{5}
    % block
    \implicant{3}{6}
  \end{cartonaugh}
  \begin{cartonaugh}[4][4][1]
    % single cell
    \implicant{0}{0}
    \implicant{1}{1}
    \implicant{2}{2}
    \implicant{3}{3}
    % horizontal
    \implicant{9}{11}
    % vertical
    \implicant{4}{12}
    % block
    \implicant{5}{15}
  \end{cartonaugh}
  \begin{cartonaugh}[4][4][2]
    % single cell
    \implicant{0}{0}
    \implicant{1}{1}
    \implicant{2}{2}
    \implicant{3}{3}
    % horizontal
    \implicant{9}{11}
    % vertical
    \implicant{4}{12}
    % block
    \implicant{5}{15}
  \end{cartonaugh}
  \begin{cartonaugh}[4][4][4]
    % single cell
    \implicant{0}{0}
    \implicant{1}{1}
    \implicant{2}{2}
    \implicant{3}{3}
    % horizontal
    \implicant{9}{11}
    % vertical
    \implicant{4}{12}
    % block
    \implicant{5}{15}
  \end{cartonaugh}
  % draw on 0th and 2nd submaps(when possible)
  \begin{cartonaugh}[2][2][1]
    % single cell
    \implicant{0}{0}[0,2]
    % horizontal
    \implicant{2}{3}[0,2]
    % vertical
    \implicant{1}{3}[0,2]
    % block
    \implicant{0}{3}[0,2]
  \end{cartonaugh}
  \begin{cartonaugh}[2][4][1]
    % single cell
    \implicant{0}{0}[0,2]
    \implicant{1}{1}[0,2]
    % horizontal
    \implicant{2}{3}[0,2]
    % vertical
    \implicant{3}{7}[0,2]
    % block
    \implicant{6}{5}[0,2]
  \end{cartonaugh}
  \begin{cartonaugh}[4][2][1]
    % single cell
    \implicant{0}{0}[0,2]
    \implicant{1}{1}[0,2]
    % horizontal
    \implicant{4}{5}[0,2]
    % vertical
    \implicant{1}{5}[0,2]
    % block
    \implicant{3}{6}[0,2]
  \end{cartonaugh}
  \begin{cartonaugh}[4][4][1]
    % single cell
    \implicant{0}{0}[0,2]
    \implicant{1}{1}[0,2]
    \implicant{2}{2}[0,2]
    \implicant{3}{3}[0,2]
    % horizontal
    \implicant{9}{11}[0,2]
    % vertical
    \implicant{4}{12}[0,2]
    % block
    \implicant{5}{15}[0,2]
  \end{cartonaugh}
  \begin{cartonaugh}[4][4][2]
    % single cell
    \implicant{0}{0}[0,2]
    \implicant{1}{1}[0,2]
    \implicant{2}{2}[0,2]
    \implicant{3}{3}[0,2]
    % horizontal
    \implicant{9}{11}[0,2]
    % vertical
    \implicant{4}{12}[0,2]
    % block
    \implicant{5}{15}[0,2]
  \end{cartonaugh}
  \begin{cartonaugh}[4][4][4]
    % single cell
    \implicant{0}{0}[0,2]
    \implicant{1}{1}[0,2]
    \implicant{2}{2}[0,2]
    \implicant{3}{3}[0,2]
    % horizontal
    \implicant{9}{11}[0,2]
    % vertical
    \implicant{4}{12}[0,2]
    % block
    \implicant{5}{15}[0,2]
  \end{cartonaugh}
  % draw multiple different implicants
  \begin{cartonaugh}[2][2][1]
    % single cell
    \implicant{0}{0}[0]
    % horizontal
    \implicant{2}{3}[0]
    % vertical
    \implicant{1}{3}[0]
    % block
    \implicant{0}{3}[0]
  \end{cartonaugh}
  \begin{cartonaugh}[2][4][1]
    % single cell
    \implicant{0}{0}[0]
    \implicant{1}{1}[0]
    % horizontal
    \implicant{2}{3}[0]
    % vertical
    \implicant{3}{7}[0]
    % block
    \implicant{6}{5}[0]
  \end{cartonaugh}
  \begin{cartonaugh}[4][2][1]
    % single cell
    \implicant{0}{0}[0]
    \implicant{1}{1}[0]
    % horizontal
    \implicant{4}{5}[0]
    % vertical
    \implicant{1}{5}[0]
    % block
    \implicant{3}{6}[0]
  \end{cartonaugh}
  \begin{cartonaugh}[4][4][1]
    % single cell
    \implicant{0}{0}[0]
    \implicant{1}{1}[0]
    \implicant{2}{2}[0]
    \implicant{3}{3}[0]
    % horizontal
    \implicant{9}{11}[0]
    % vertical
    \implicant{4}{12}[0]
    % block
    \implicant{5}{15}[0]
  \end{cartonaugh}
  \begin{cartonaugh}[4][4][2]
    % single cell
    \implicant{0}{0}[0]
    \implicant{1}{1}[0]
    \implicant{2}{2}[0]
    \implicant{3}{3}[0]
    \implicant{0}{0}[1]
    \implicant{1}{1}[1]
    \implicant{2}{2}[1]
    \implicant{3}{3}[1]
    % horizontal
    \implicant{9}{11}[0]
    \implicant{9}{11}[1]
    % vertical
    \implicant{4}{12}[0]
    \implicant{4}{12}[1]
    % block
    \implicant{5}{15}[0]
    \implicant{5}{15}[1]
  \end{cartonaugh}
  \begin{cartonaugh}[4][4][4]
    % single cell
    \implicant{0}{0}[0]
    \implicant{1}{1}[0]
    \implicant{2}{2}[0]
    \implicant{3}{3}[0]
    \implicant{0}{0}[1]
    \implicant{1}{1}[1]
    \implicant{2}{2}[1]
    \implicant{3}{3}[1]
    \implicant{0}{0}[2]
    \implicant{1}{1}[2]
    \implicant{2}{2}[2]
    \implicant{3}{3}[2]
    \implicant{0}{0}[3]
    \implicant{1}{1}[3]
    \implicant{2}{2}[3]
    \implicant{3}{3}[3]
    % horizontal
    \implicant{9}{11}[0]
    \implicant{9}{11}[1]
    \implicant{9}{11}[2]
    \implicant{9}{11}[3]
    % vertical
    \implicant{4}{12}[0]
    \implicant{4}{12}[1]
    \implicant{4}{12}[2]
    \implicant{4}{12}[3]
    % block
    \implicant{5}{15}[0]
    \implicant{5}{15}[1]
    \implicant{5}{15}[2]
    \implicant{5}{15}[3]
  \end{cartonaugh}
\end{document}