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Known man-made solutions are listed in table below.
Legend: [http://www.mat.univie.ac.at/~neum/ms/zauner.pdf Zauner], [http://arxiv.org/abs/quant-ph/0310075 RKSC],
[http://arxiv.org/abs/quant-ph/0412001 Marcus],
Marcus+=Marcus has/believes he could easily produce a solution.
{| class="wikitable"
|-
! Dimension
! Who
|-
| 2,3 || Many
|-
| 4 || Zauner, RKSC
|-
| 5 || Zauner
|-
| 6 || Marcus+
|-
| 7 || Marcus
|-
| 8 || Hoggart
|-
|9 || Marcus+
|-
|12 || Marcus+
|-
|15 || Marcus+
|-
| 19 || Marcus
|}
