The 253 8-subsets of [24] which contains 1 from the Witt design:

[1, 2, 3, 4, 5, 6, 7, 8]
[1, 2, 3, 4, 9, 10, 11, 12]
[1, 2, 3, 4, 13, 14, 15, 16]
[1, 2, 3, 4, 17, 18, 19, 20]
[1, 2, 3, 4, 21, 22, 23, 24]
[1, 2, 3, 5, 9, 13, 17, 21]
[1, 2, 3, 5, 10, 14, 18, 22]
[1, 2, 3, 5, 11, 15, 19, 23]
[1, 2, 3, 5, 12, 16, 20, 24]
[1, 2, 3, 6, 9, 14, 19, 24]

[1, 2, 3, 6, 10, 13, 20, 23]
[1, 2, 3, 6, 11, 16, 17, 22]
[1, 2, 3, 6, 12, 15, 18, 21]
[1, 2, 3, 7, 9, 15, 20, 22]
[1, 2, 3, 7, 10, 16, 19, 21]
[1, 2, 3, 7, 11, 13, 18, 24]
[1, 2, 3, 7, 12, 14, 17, 23]
[1, 2, 3, 8, 9, 16, 18, 23]
[1, 2, 3, 8, 10, 15, 17, 24]
[1, 2, 3, 8, 11, 14, 20, 21]

[1, 2, 3, 8, 12, 13, 19, 22]
[1, 2, 4, 5, 9, 14, 20, 23]
[1, 2, 4, 5, 10, 13, 19, 24]
[1, 2, 4, 5, 11, 16, 18, 21]
[1, 2, 4, 5, 12, 15, 17, 22]
[1, 2, 4, 6, 9, 13, 18, 22]
[1, 2, 4, 6, 10, 14, 17, 21]
[1, 2, 4, 6, 11, 15, 20, 24]
[1, 2, 4, 6, 12, 16, 19, 23]
[1, 2, 4, 7, 9, 16, 17, 24]

[1, 2, 4, 7, 10, 15, 18, 23]
[1, 2, 4, 7, 11, 14, 19, 22]
[1, 2, 4, 7, 12, 13, 20, 21]
[1, 2, 4, 8, 9, 15, 19, 21]
[1, 2, 4, 8, 10, 16, 20, 22]
[1, 2, 4, 8, 11, 13, 17, 23]
[1, 2, 4, 8, 12, 14, 18, 24]
[1, 2, 5, 6, 9, 10, 15, 16]
[1, 2, 5, 6, 11, 12, 13, 14]
[1, 2, 5, 6, 17, 18, 23, 24]

[1, 2, 5, 6, 19, 20, 21, 22]
[1, 2, 5, 7, 9, 12, 18, 19]
[1, 2, 5, 7, 10, 11, 17, 20]
[1, 2, 5, 7, 13, 16, 22, 23]
[1, 2, 5, 7, 14, 15, 21, 24]
[1, 2, 5, 8, 9, 11, 22, 24]
[1, 2, 5, 8, 10, 12, 21, 23]
[1, 2, 5, 8, 13, 15, 18, 20]
[1, 2, 5, 8, 14, 16, 17, 19]
[1, 2, 6, 7, 9, 11, 21, 23]

[1, 2, 6, 7, 10, 12, 22, 24]
[1, 2, 6, 7, 13, 15, 17, 19]
[1, 2, 6, 7, 14, 16, 18, 20]
[1, 2, 6, 8, 9, 12, 17, 20]
[1, 2, 6, 8, 10, 11, 18, 19]
[1, 2, 6, 8, 13, 16, 21, 24]
[1, 2, 6, 8, 14, 15, 22, 23]
[1, 2, 7, 8, 9, 10, 13, 14]
[1, 2, 7, 8, 11, 12, 15, 16]
[1, 2, 7, 8, 17, 18, 21, 22]

[1, 2, 7, 8, 19, 20, 23, 24]
[1, 2, 9, 10, 17, 19, 22, 23]
[1, 2, 9, 10, 18, 20, 21, 24]
[1, 2, 9, 11, 13, 16, 19, 20]
[1, 2, 9, 11, 14, 15, 17, 18]
[1, 2, 9, 12, 13, 15, 23, 24]
[1, 2, 9, 12, 14, 16, 21, 22]
[1, 2, 10, 11, 13, 15, 21, 22]
[1, 2, 10, 11, 14, 16, 23, 24]
[1, 2, 10, 12, 13, 16, 17, 18]

[1, 2, 10, 12, 14, 15, 19, 20]
[1, 2, 11, 12, 17, 19, 21, 24]
[1, 2, 11, 12, 18, 20, 22, 23]
[1, 2, 13, 14, 17, 20, 22, 24]
[1, 2, 13, 14, 18, 19, 21, 23]
[1, 2, 15, 16, 17, 20, 21, 23]
[1, 2, 15, 16, 18, 19, 22, 24]
[1, 3, 4, 5, 9, 15, 18, 24]
[1, 3, 4, 5, 10, 16, 17, 23]
[1, 3, 4, 5, 11, 13, 20, 22]

[1, 3, 4, 5, 12, 14, 19, 21]
[1, 3, 4, 6, 9, 16, 20, 21]
[1, 3, 4, 6, 10, 15, 19, 22]
[1, 3, 4, 6, 11, 14, 18, 23]
[1, 3, 4, 6, 12, 13, 17, 24]
[1, 3, 4, 7, 9, 13, 19, 23]
[1, 3, 4, 7, 10, 14, 20, 24]
[1, 3, 4, 7, 11, 15, 17, 21]
[1, 3, 4, 7, 12, 16, 18, 22]
[1, 3, 4, 8, 9, 14, 17, 22]

[1, 3, 4, 8, 10, 13, 18, 21]
[1, 3, 4, 8, 11, 16, 19, 24]
[1, 3, 4, 8, 12, 15, 20, 23]
[1, 3, 5, 6, 9, 12, 22, 23]
[1, 3, 5, 6, 10, 11, 21, 24]
[1, 3, 5, 6, 13, 16, 18, 19]
[1, 3, 5, 6, 14, 15, 17, 20]
[1, 3, 5, 7, 9, 11, 14, 16]
[1, 3, 5, 7, 10, 12, 13, 15]
[1, 3, 5, 7, 17, 19, 22, 24]

[1, 3, 5, 7, 18, 20, 21, 23]
[1, 3, 5, 8, 9, 10, 19, 20]
[1, 3, 5, 8, 11, 12, 17, 18]
[1, 3, 5, 8, 13, 14, 23, 24]
[1, 3, 5, 8, 15, 16, 21, 22]
[1, 3, 6, 7, 9, 10, 17, 18]
[1, 3, 6, 7, 11, 12, 19, 20]
[1, 3, 6, 7, 13, 14, 21, 22]
[1, 3, 6, 7, 15, 16, 23, 24]
[1, 3, 6, 8, 9, 11, 13, 15]

[1, 3, 6, 8, 10, 12, 14, 16]
[1, 3, 6, 8, 17, 19, 21, 23]
[1, 3, 6, 8, 18, 20, 22, 24]
[1, 3, 7, 8, 9, 12, 21, 24]
[1, 3, 7, 8, 10, 11, 22, 23]
[1, 3, 7, 8, 13, 16, 17, 20]
[1, 3, 7, 8, 14, 15, 18, 19]
[1, 3, 9, 10, 13, 16, 22, 24]
[1, 3, 9, 10, 14, 15, 21, 23]
[1, 3, 9, 11, 17, 20, 23, 24]

[1, 3, 9, 11, 18, 19, 21, 22]
[1, 3, 9, 12, 13, 14, 18, 20]
[1, 3, 9, 12, 15, 16, 17, 19]
[1, 3, 10, 11, 13, 14, 17, 19]
[1, 3, 10, 11, 15, 16, 18, 20]
[1, 3, 10, 12, 17, 20, 21, 22]
[1, 3, 10, 12, 18, 19, 23, 24]
[1, 3, 11, 12, 13, 16, 21, 23]
[1, 3, 11, 12, 14, 15, 22, 24]
[1, 3, 13, 15, 17, 18, 22, 23]

[1, 3, 13, 15, 19, 20, 21, 24]
[1, 3, 14, 16, 17, 18, 21, 24]
[1, 3, 14, 16, 19, 20, 22, 23]
[1, 4, 5, 6, 9, 11, 17, 19]
[1, 4, 5, 6, 10, 12, 18, 20]
[1, 4, 5, 6, 13, 15, 21, 23]
[1, 4, 5, 6, 14, 16, 22, 24]
[1, 4, 5, 7, 9, 10, 21, 22]
[1, 4, 5, 7, 11, 12, 23, 24]
[1, 4, 5, 7, 13, 14, 17, 18]

[1, 4, 5, 7, 15, 16, 19, 20]
[1, 4, 5, 8, 9, 12, 13, 16]
[1, 4, 5, 8, 10, 11, 14, 15]
[1, 4, 5, 8, 17, 20, 21, 24]
[1, 4, 5, 8, 18, 19, 22, 23]
[1, 4, 6, 7, 9, 12, 14, 15]
[1, 4, 6, 7, 10, 11, 13, 16]
[1, 4, 6, 7, 17, 20, 22, 23]
[1, 4, 6, 7, 18, 19, 21, 24]
[1, 4, 6, 8, 9, 10, 23, 24]

[1, 4, 6, 8, 11, 12, 21, 22]
[1, 4, 6, 8, 13, 14, 19, 20]
[1, 4, 6, 8, 15, 16, 17, 18]
[1, 4, 7, 8, 9, 11, 18, 20]
[1, 4, 7, 8, 10, 12, 17, 19]
[1, 4, 7, 8, 13, 15, 22, 24]
[1, 4, 7, 8, 14, 16, 21, 23]
[1, 4, 9, 10, 13, 15, 17, 20]
[1, 4, 9, 10, 14, 16, 18, 19]
[1, 4, 9, 11, 13, 14, 21, 24]

[1, 4, 9, 11, 15, 16, 22, 23]
[1, 4, 9, 12, 17, 18, 21, 23]
[1, 4, 9, 12, 19, 20, 22, 24]
[1, 4, 10, 11, 17, 18, 22, 24]
[1, 4, 10, 11, 19, 20, 21, 23]
[1, 4, 10, 12, 13, 14, 22, 23]
[1, 4, 10, 12, 15, 16, 21, 24]
[1, 4, 11, 12, 13, 15, 18, 19]
[1, 4, 11, 12, 14, 16, 17, 20]
[1, 4, 13, 16, 17, 19, 21, 22]

[1, 4, 13, 16, 18, 20, 23, 24]
[1, 4, 14, 15, 17, 19, 23, 24]
[1, 4, 14, 15, 18, 20, 21, 22]
[1, 5, 6, 7, 9, 13, 20, 24]
[1, 5, 6, 7, 10, 14, 19, 23]
[1, 5, 6, 7, 11, 15, 18, 22]
[1, 5, 6, 7, 12, 16, 17, 21]
[1, 5, 6, 8, 9, 14, 18, 21]
[1, 5, 6, 8, 10, 13, 17, 22]
[1, 5, 6, 8, 11, 16, 20, 23]

[1, 5, 6, 8, 12, 15, 19, 24]
[1, 5, 7, 8, 9, 15, 17, 23]
[1, 5, 7, 8, 10, 16, 18, 24]
[1, 5, 7, 8, 11, 13, 19, 21]
[1, 5, 7, 8, 12, 14, 20, 22]
[1, 5, 9, 10, 11, 13, 18, 23]
[1, 5, 9, 10, 12, 14, 17, 24]
[1, 5, 9, 11, 12, 15, 20, 21]
[1, 5, 9, 13, 14, 15, 19, 22]
[1, 5, 9, 16, 17, 18, 20, 22]

[1, 5, 9, 16, 19, 21, 23, 24]
[1, 5, 10, 11, 12, 16, 19, 22]
[1, 5, 10, 13, 14, 16, 20, 21]
[1, 5, 10, 15, 17, 18, 19, 21]
[1, 5, 10, 15, 20, 22, 23, 24]
[1, 5, 11, 13, 15, 16, 17, 24]
[1, 5, 11, 14, 17, 21, 22, 23]
[1, 5, 11, 14, 18, 19, 20, 24]
[1, 5, 12, 13, 17, 19, 20, 23]
[1, 5, 12, 13, 18, 21, 22, 24]

[1, 5, 12, 14, 15, 16, 18, 23]
[1, 6, 7, 8, 9, 16, 19, 22]
[1, 6, 7, 8, 10, 15, 20, 21]
[1, 6, 7, 8, 11, 14, 17, 24]
[1, 6, 7, 8, 12, 13, 18, 23]
[1, 6, 9, 10, 11, 14, 20, 22]
[1, 6, 9, 10, 12, 13, 19, 21]
[1, 6, 9, 11, 12, 16, 18, 24]
[1, 6, 9, 13, 14, 16, 17, 23]
[1, 6, 9, 15, 17, 21, 22, 24]

[1, 6, 9, 15, 18, 19, 20, 23]
[1, 6, 10, 11, 12, 15, 17, 23]
[1, 6, 10, 13, 14, 15, 18, 24]
[1, 6, 10, 16, 17, 19, 20, 24]
[1, 6, 10, 16, 18, 21, 22, 23]
[1, 6, 11, 13, 17, 18, 20, 21]
[1, 6, 11, 13, 19, 22, 23, 24]
[1, 6, 11, 14, 15, 16, 19, 21]
[1, 6, 12, 13, 15, 16, 20, 22]
[1, 6, 12, 14, 17, 18, 19, 22]

[1, 6, 12, 14, 20, 21, 23, 24]
[1, 7, 9, 10, 11, 15, 19, 24]
[1, 7, 9, 10, 12, 16, 20, 23]
[1, 7, 9, 11, 12, 13, 17, 22]
[1, 7, 9, 13, 15, 16, 18, 21]
[1, 7, 9, 14, 17, 19, 20, 21]
[1, 7, 9, 14, 18, 22, 23, 24]
[1, 7, 10, 11, 12, 14, 18, 21]
[1, 7, 10, 13, 17, 21, 23, 24]
[1, 7, 10, 13, 18, 19, 20, 22]

[1, 7, 10, 14, 15, 16, 17, 22]
[1, 7, 11, 13, 14, 15, 20, 23]
[1, 7, 11, 16, 17, 18, 19, 23]
[1, 7, 11, 16, 20, 21, 22, 24]
[1, 7, 12, 13, 14, 16, 19, 24]
[1, 7, 12, 15, 17, 18, 20, 24]
[1, 7, 12, 15, 19, 21, 22, 23]
[1, 8, 9, 10, 11, 16, 17, 21]
[1, 8, 9, 10, 12, 15, 18, 22]
[1, 8, 9, 11, 12, 14, 19, 23]

[1, 8, 9, 13, 17, 18, 19, 24]
[1, 8, 9, 13, 20, 21, 22, 23]
[1, 8, 9, 14, 15, 16, 20, 24]
[1, 8, 10, 11, 12, 13, 20, 24]
[1, 8, 10, 13, 15, 16, 19, 23]
[1, 8, 10, 14, 17, 18, 20, 23]
[1, 8, 10, 14, 19, 21, 22, 24]
[1, 8, 11, 13, 14, 16, 18, 22]
[1, 8, 11, 15, 17, 19, 20, 22]
[1, 8, 11, 15, 18, 21, 23, 24]

[1, 8, 12, 13, 14, 15, 17, 21]
[1, 8, 12, 16, 17, 22, 23, 24]
[1, 8, 12, 16, 18, 19, 20, 21]