\end{array}$        \end{array}$        \end{array}$        \end{array}$        \end{array}$        \end{array}$        \end{array}$        \end{array}$        \end{array}$        \end{array}$        \end{array}$        \end{array}$        \end{array}$        \end{array}$        \end{array}$
  -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

  : Partition of the 2-subspaces of ${{\mathbb{F}}}_2^4$ into the sets ${{\cal A}}$. ${{\cal B}}$, and ${{\cal C}}$[]{data-label="tab:partition"}

  -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
    ${{\cal Y}}_1$      ${{\cal Y}}_2$      ${{\cal Y}}_3$      ${{\cal Y}}_4$      ${{\cal Y}}_5$      ${{\cal Y}}_6$      ${{\cal Y}}_7$      ${{\cal Y}}_8$      ${{\cal Y}}_9$     ${{\cal Y}}_{10}$   ${{\cal Y}}_{11}$   ${{\cal Y}}_{12}$   ${{\cal Y}}_{13}$   ${{\cal Y}}_{14}$   ${{\cal Y}}_{15}$
  ------------------- ------------------- ------------------- ------------------- ------------------- ------------------- ------------------- ------------------- ------------------- ------------------- ------------------- ------------------- ------------------- ------------------- -------------------
   $\begin{array}{c}   $\begin{array}{c}   $\begin{array}{c}   $\begin{array}{c}   $\begin{array}{c}   $\begin{array}{c}   $\begin{array}{c}   $\begin{array}{c}   $\begin{array}{c}   $\begin{array}{c}   $\begin{array}{c}   $\begin{array}{c}   $\begin{array}{c}   $\begin{array}{c}   $\begin{array}{c}
        000 \\              001 \\              001 \\              010 \\              010 \\              010 \\              010 \\              010 \\              010 \\              010 \\              010 \\              010 \\              010 \\              010 \\              010 \\
        010 \\              010 \\              010 \\              011 \\              010 \\              011 \\              100 \\              100 \\              100 \\              100 \\              100 \\              100 \\              000 \\              001 \\              001 \\
        011 \\              010 \\              011 \\              100 \\              100 \\              100 \\              010 \\              011 \\              011 \\              000 \\              001 \\              001 \\              100 \\              100 \\              100 \\
          100                 100                 100                 000                 001                 001                 011                 011                 010                 101                 100                 101                 111                 110                 111
     \end{array}$        