The rows of this matrix are 16 of the 16*24 = 384 permutations in the symmetry group of the tesseract.
The sequence in row ${\displaystyle m}$ of matrix ${\displaystyle n}$ is the result of applying permutation ${\displaystyle (m,n)}$ on the natural order.
The fixed points (places where permuted sequence equals the natural order) are highlighted in red.

The letters an negators on the left encode the permutation in that row.
Compare these cube permutations to see how. (E.g. cube 3 to matrix 3.)

The top rows have no negators, and are shown in this matrix.