14 stages, 4 taps:  (21 sets)

[14, 13, 12, 2]
[14, 13, 11, 9]
[14, 13, 11, 4]
[14, 13, 10, 8]
[14, 13, 10, 6]
[14, 13, 10, 3]
[14, 13, 8, 6]
[14, 13, 8, 4]
[14, 13, 8, 3]
[14, 13, 7, 3]
[14, 13, 4, 2]
[14, 13, 3, 2]
[14, 12, 11, 6]
[14, 12, 11, 5]
[14, 12, 9, 2]
[14, 12, 7, 5]
[14, 11, 10, 9]
[14, 11, 10, 3]
[14, 11, 9, 7]
[14, 11, 6, 5]
[14, 9, 8, 5]


14 stages, 6 taps:  (113 sets)

[14, 13, 12, 11, 10, 8]
[14, 13, 12, 11, 10, 2]
[14, 13, 12, 11, 9, 7]
[14, 13, 12, 11, 9, 1]
[14, 13, 12, 11, 8, 7]
[14, 13, 12, 11, 5, 4]
[14, 13, 12, 11, 5, 2]
[14, 13, 12, 11, 4, 2]
[14, 13, 12, 10, 8, 5]
[14, 13, 12, 10, 4, 2]
[14, 13, 12, 10, 4, 1]
[14, 13, 12, 9, 8, 3]
[14, 13, 12, 9, 8, 1]
[14, 13, 12, 9, 7, 6]
[14, 13, 12, 9, 5, 4]
[14, 13, 12, 8, 7, 5]
[14, 13, 12, 8, 5, 4]
[14, 13, 12, 8, 4, 3]
[14, 13, 12, 8, 4, 2]
[14, 13, 12, 8, 4, 1]
[14, 13, 12, 7, 6, 5]
[14, 13, 12, 7, 6, 3]
[14, 13, 12, 7, 5, 3]
[14, 13, 12, 5, 4, 1]
[14, 13, 12, 4, 3, 2]
[14, 13, 11, 10, 9, 8]
[14, 13, 11, 10, 9, 7]
[14, 13, 11, 10, 9, 6]
[14, 13, 11, 10, 9, 3]
[14, 13, 11, 10, 8, 3]
[14, 13, 11, 10, 7, 6]
[14, 13, 11, 9, 8, 7]
[14, 13, 11, 9, 8, 1]
[14, 13, 11, 9, 7, 1]
[14, 13, 11, 9, 6, 4]
[14, 13, 11, 8, 7, 5]
[14, 13, 11, 8, 4, 3]
[14, 13, 11, 7, 6, 2]
[14, 13, 11, 7, 5, 3]
[14, 13, 11, 7, 5, 2]
[14, 13, 11, 7, 4, 1]
[14, 13, 11, 6, 4, 1]
[14, 13, 11, 4, 3, 2]
[14, 13, 10, 9, 8, 7]
[14, 13, 10, 9, 8, 4]
[14, 13, 10, 9, 7, 1]
[14, 13, 10, 9, 5, 1]
[14, 13, 10, 9, 3, 2]
[14, 13, 10, 8, 7, 4]
[14, 13, 10, 8, 6, 2]
[14, 13, 9, 8, 7, 5]
[14, 13, 9, 8, 7, 4]
[14, 13, 9, 8, 7, 3]
[14, 13, 9, 8, 5, 4]
[14, 13, 9, 8, 5, 1]
[14, 13, 9, 7, 5, 3]
[14, 13, 9, 7, 5, 2]
[14, 13, 9, 7, 3, 2]
[14, 13, 8, 7, 5, 2]
[14, 13, 8, 5, 4, 3]
[14, 13, 8, 5, 3, 2]
[14, 13, 7, 6, 4, 2]
[14, 13, 7, 5, 4, 3]
[14, 13, 7, 4, 3, 2]
[14, 13, 5, 4, 3, 2]
[14, 12, 11, 10, 9, 7]
[14, 12, 11, 10, 8, 2]
[14, 12, 11, 10, 7, 6]
[14, 12, 11, 10, 7, 5]
[14, 12, 11, 10, 6, 3]
[14, 12, 11, 10, 5, 4]
[14, 12, 11, 10, 4, 3]
[14, 12, 11, 9, 7, 6]
[14, 12, 11, 9, 6, 3]
[14, 12, 11, 9, 6, 2]
[14, 12, 11, 9, 5, 2]
[14, 12, 11, 8, 7, 5]
[14, 12, 11, 7, 4, 3]
[14, 12, 11, 7, 4, 2]
[14, 12, 11, 5, 4, 2]
[14, 12, 10, 9, 7, 6]
[14, 12, 10, 9, 5, 4]
[14, 12, 10, 9, 5, 3]
[14, 12, 10, 9, 4, 2]
[14, 12, 10, 8, 7, 6]
[14, 12, 10, 8, 7, 4]
[14, 12, 10, 8, 7, 2]
[14, 12, 10, 8, 4, 3]
[14, 12, 10, 7, 6, 5]
[14, 12, 10, 5, 4, 3]
[14, 12, 9, 8, 5, 3]
[14, 12, 9, 8, 5, 2]
[14, 12, 9, 7, 6, 4]
[14, 12, 9, 7, 6, 2]
[14, 12, 9, 7, 5, 4]
[14, 12, 9, 7, 4, 3]
[14, 12, 8, 7, 6, 4]
[14, 12, 8, 7, 5, 4]
[14, 12, 8, 7, 4, 3]
[14, 12, 8, 6, 4, 3]
[14, 12, 7, 6, 5, 3]
[14, 11, 10, 9, 6, 4]
[14, 11, 10, 9, 6, 3]
[14, 11, 10, 8, 7, 6]
[14, 11, 10, 8, 6, 4]
[14, 11, 10, 8, 5, 4]
[14, 11, 10, 7, 6, 4]
[14, 11, 9, 8, 7, 5]
[14, 11, 9, 8, 6, 3]
[14, 11, 9, 7, 6, 3]
[14, 11, 8, 7, 6, 5]
[14, 10, 9, 8, 7, 6]
[14, 10, 9, 8, 5, 4]


14 stages, 8 taps:  (169 sets)

[14, 13, 12, 11, 10, 9, 8, 5]
[14, 13, 12, 11, 10, 9, 8, 3]
[14, 13, 12, 11, 10, 9, 6, 5]
[14, 13, 12, 11, 10, 9, 4, 3]
[14, 13, 12, 11, 10, 9, 3, 2]
[14, 13, 12, 11, 10, 8, 7, 4]
[14, 13, 12, 11, 10, 8, 6, 2]
[14, 13, 12, 11, 10, 8, 4, 2]
[14, 13, 12, 11, 10, 7, 6, 4]
[14, 13, 12, 11, 10, 7, 6, 1]
[14, 13, 12, 11, 10, 7, 5, 1]
[14, 13, 12, 11, 10, 7, 4, 2]
[14, 13, 12, 11, 10, 7, 4, 1]
[14, 13, 12, 11, 10, 7, 3, 1]
[14, 13, 12, 11, 10, 6, 4, 3]
[14, 13, 12, 11, 10, 5, 3, 2]
[14, 13, 12, 11, 10, 5, 2, 1]
[14, 13, 12, 11, 9, 8, 7, 5]
[14, 13, 12, 11, 9, 8, 6, 4]
[14, 13, 12, 11, 9, 8, 5, 1]
[14, 13, 12, 11, 9, 7, 6, 5]
[14, 13, 12, 11, 9, 7, 6, 1]
[14, 13, 12, 11, 9, 7, 3, 2]
[14, 13, 12, 11, 9, 6, 4, 2]
[14, 13, 12, 11, 9, 6, 3, 1]
[14, 13, 12, 11, 9, 5, 4, 2]
[14, 13, 12, 11, 9, 5, 3, 1]
[14, 13, 12, 11, 9, 4, 3, 1]
[14, 13, 12, 11, 8, 7, 6, 3]
[14, 13, 12, 11, 8, 7, 5, 4]
[14, 13, 12, 11, 8, 7, 2, 1]
[14, 13, 12, 11, 8, 6, 5, 4]
[14, 13, 12, 11, 8, 6, 4, 3]
[14, 13, 12, 11, 8, 6, 3, 2]
[14, 13, 12, 11, 8, 5, 2, 1]
[14, 13, 12, 11, 8, 4, 2, 1]
[14, 13, 12, 11, 7, 6, 4, 3]
[14, 13, 12, 11, 7, 6, 3, 2]
[14, 13, 12, 11, 7, 6, 3, 1]
[14, 13, 12, 11, 6, 5, 3, 2]
[14, 13, 12, 11, 5, 4, 3, 2]
[14, 13, 12, 10, 9, 8, 6, 3]
[14, 13, 12, 10, 9, 8, 3, 1]
[14, 13, 12, 10, 9, 7, 6, 4]
[14, 13, 12, 10, 9, 7, 5, 1]
[14, 13, 12, 10, 9, 6, 5, 3]
[14, 13, 12, 10, 9, 6, 5, 1]
[14, 13, 12, 10, 9, 6, 4, 2]
[14, 13, 12, 10, 9, 6, 4, 1]
[14, 13, 12, 10, 9, 6, 2, 1]
[14, 13, 12, 10, 9, 5, 4, 3]
[14, 13, 12, 10, 8, 7, 6, 4]
[14, 13, 12, 10, 8, 7, 5, 1]
[14, 13, 12, 10, 8, 7, 4, 3]
[14, 13, 12, 10, 8, 4, 3, 1]
[14, 13, 12, 10, 7, 6, 5, 3]
[14, 13, 12, 10, 7, 6, 3, 2]
[14, 13, 12, 10, 7, 5, 4, 1]
[14, 13, 12, 10, 7, 5, 3, 1]
[14, 13, 12, 10, 6, 5, 3, 2]
[14, 13, 12, 10, 6, 5, 3, 1]
[14, 13, 12, 10, 6, 4, 3, 1]
[14, 13, 12, 9, 8, 7, 6, 4]
[14, 13, 12, 9, 8, 7, 5, 2]
[14, 13, 12, 9, 8, 7, 4, 1]
[14, 13, 12, 9, 8, 7, 3, 2]
[14, 13, 12, 9, 8, 5, 3, 1]
[14, 13, 12, 9, 8, 5, 2, 1]
[14, 13, 12, 9, 7, 6, 5, 4]
[14, 13, 12, 9, 7, 6, 5, 2]
[14, 13, 12, 9, 7, 6, 3, 2]
[14, 13, 12, 9, 7, 5, 4, 1]
[14, 13, 12, 9, 5, 4, 3, 1]
[14, 13, 12, 8, 7, 6, 5, 2]
[14, 13, 12, 8, 7, 5, 4, 2]
[14, 13, 12, 8, 7, 4, 3, 1]
[14, 13, 12, 8, 6, 5, 3, 1]
[14, 13, 12, 8, 5, 4, 3, 2]
[14, 13, 12, 7, 5, 4, 3, 1]
[14, 13, 12, 6, 5, 4, 3, 2]
[14, 13, 11, 10, 9, 8, 7, 4]
[14, 13, 11, 10, 9, 8, 5, 4]
[14, 13, 11, 10, 9, 8, 5, 3]
[14, 13, 11, 10, 9, 8, 4, 2]
[14, 13, 11, 10, 9, 7, 6, 1]
[14, 13, 11, 10, 9, 7, 4, 2]
[14, 13, 11, 10, 9, 6, 4, 1]
[14, 13, 11, 10, 9, 5, 4, 1]
[14, 13, 11, 10, 9, 5, 3, 2]
[14, 13, 11, 10, 8, 7, 6, 2]
[14, 13, 11, 10, 8, 7, 5, 4]
[14, 13, 11, 10, 8, 7, 5, 1]
[14, 13, 11, 10, 8, 6, 5, 3]
[14, 13, 11, 10, 8, 6, 5, 2]
[14, 13, 11, 10, 8, 6, 5, 1]
[14, 13, 11, 10, 8, 6, 4, 1]
[14, 13, 11, 10, 8, 5, 3, 1]
[14, 13, 11, 10, 7, 6, 5, 2]
[14, 13, 11, 10, 7, 5, 4, 3]
[14, 13, 11, 10, 7, 5, 4, 2]
[14, 13, 11, 10, 6, 5, 4, 1]
[14, 13, 11, 10, 5, 4, 3, 2]
[14, 13, 11, 9, 8, 7, 6, 5]
[14, 13, 11, 9, 8, 7, 6, 2]
[14, 13, 11, 9, 8, 7, 3, 2]
[14, 13, 11, 9, 8, 6, 5, 3]
[14, 13, 11, 9, 8, 6, 3, 1]
[14, 13, 11, 9, 8, 5, 4, 3]
[14, 13, 11, 9, 8, 5, 4, 1]
[14, 13, 11, 9, 8, 5, 3, 1]
[14, 13, 11, 9, 7, 6, 5, 3]
[14, 13, 11, 9, 7, 6, 3, 1]
[14, 13, 11, 9, 7, 5, 4, 2]
[14, 13, 11, 9, 7, 5, 4, 1]
[14, 13, 11, 9, 6, 5, 4, 2]
[14, 13, 11, 9, 6, 5, 3, 2]
[14, 13, 11, 8, 7, 6, 5, 3]
[14, 13, 11, 8, 7, 4, 3, 2]
[14, 13, 11, 8, 6, 5, 4, 1]
[14, 13, 10, 9, 8, 7, 6, 4]
[14, 13, 10, 9, 8, 7, 5, 1]
[14, 13, 10, 9, 8, 6, 5, 3]
[14, 13, 10, 9, 7, 6, 4, 3]
[14, 13, 10, 9, 7, 5, 4, 2]
[14, 13, 10, 9, 6, 4, 3, 2]
[14, 13, 10, 8, 7, 6, 4, 2]
[14, 13, 10, 8, 7, 5, 4, 3]
[14, 13, 10, 8, 7, 5, 3, 2]
[14, 13, 10, 7, 6, 5, 4, 2]
[14, 13, 9, 8, 6, 5, 4, 2]
[14, 13, 9, 8, 6, 5, 3, 2]
[14, 13, 9, 7, 6, 4, 3, 2]
[14, 13, 9, 6, 5, 4, 3, 2]
[14, 13, 8, 7, 6, 5, 4, 2]
[14, 13, 8, 7, 6, 5, 3, 2]
[14, 13, 8, 6, 5, 4, 3, 2]
[14, 12, 11, 10, 9, 8, 6, 5]
[14, 12, 11, 10, 9, 8, 6, 2]
[14, 12, 11, 10, 9, 8, 4, 3]
[14, 12, 11, 10, 9, 7, 4, 3]
[14, 12, 11, 10, 9, 5, 3, 2]
[14, 12, 11, 10, 8, 7, 5, 3]
[14, 12, 11, 10, 8, 7, 4, 2]
[14, 12, 11, 10, 8, 7, 3, 2]
[14, 12, 11, 10, 8, 4, 3, 2]
[14, 12, 11, 10, 7, 6, 5, 2]
[14, 12, 11, 10, 7, 6, 3, 2]
[14, 12, 11, 10, 6, 5, 4, 3]
[14, 12, 11, 9, 8, 7, 6, 5]
[14, 12, 11, 9, 8, 7, 6, 2]
[14, 12, 11, 9, 8, 7, 4, 3]
[14, 12, 11, 9, 8, 6, 5, 3]
[14, 12, 11, 9, 8, 5, 4, 3]
[14, 12, 11, 9, 7, 6, 4, 3]
[14, 12, 11, 9, 7, 6, 4, 2]
[14, 12, 11, 9, 7, 5, 4, 2]
[14, 12, 11, 9, 6, 5, 4, 2]
[14, 12, 11, 8, 7, 6, 5, 3]
[14, 12, 11, 8, 7, 5, 4, 2]
[14, 12, 10, 9, 8, 7, 6, 2]
[14, 12, 10, 9, 8, 6, 4, 3]
[14, 12, 10, 8, 7, 6, 5, 3]
[14, 12, 10, 8, 6, 5, 4, 3]
[14, 12, 9, 8, 7, 6, 5, 4]
[14, 12, 9, 8, 7, 5, 4, 3]
[14, 11, 10, 9, 8, 7, 5, 3]
[14, 11, 10, 9, 8, 6, 5, 3]
[14, 11, 10, 9, 7, 6, 5, 3]
[14, 11, 9, 8, 7, 6, 5, 4]


14 stages, 10 taps:  (70 sets)

[14, 13, 12, 11, 10, 9, 8, 7, 6, 4]
[14, 13, 12, 11, 10, 9, 8, 7, 6, 2]
[14, 13, 12, 11, 10, 9, 8, 7, 3, 2]
[14, 13, 12, 11, 10, 9, 8, 7, 3, 1]
[14, 13, 12, 11, 10, 9, 8, 6, 5, 4]
[14, 13, 12, 11, 10, 9, 8, 6, 4, 2]
[14, 13, 12, 11, 10, 9, 8, 6, 3, 2]
[14, 13, 12, 11, 10, 9, 7, 6, 5, 2]
[14, 13, 12, 11, 10, 9, 7, 6, 5, 1]
[14, 13, 12, 11, 10, 9, 7, 6, 4, 1]
[14, 13, 12, 11, 10, 9, 7, 5, 3, 1]
[14, 13, 12, 11, 10, 9, 7, 4, 3, 2]
[14, 13, 12, 11, 10, 9, 6, 5, 4, 2]
[14, 13, 12, 11, 10, 9, 5, 3, 2, 1]
[14, 13, 12, 11, 10, 8, 7, 6, 5, 3]
[14, 13, 12, 11, 10, 8, 7, 6, 3, 2]
[14, 13, 12, 11, 10, 8, 7, 6, 2, 1]
[14, 13, 12, 11, 10, 8, 7, 5, 4, 1]
[14, 13, 12, 11, 10, 8, 7, 5, 2, 1]
[14, 13, 12, 11, 10, 8, 7, 4, 2, 1]
[14, 13, 12, 11, 10, 8, 6, 5, 4, 3]
[14, 13, 12, 11, 10, 8, 6, 5, 4, 1]
[14, 13, 12, 11, 10, 8, 5, 4, 2, 1]
[14, 13, 12, 11, 10, 7, 6, 5, 4, 3]
[14, 13, 12, 11, 10, 7, 5, 4, 2, 1]
[14, 13, 12, 11, 9, 8, 7, 6, 5, 4]
[14, 13, 12, 11, 9, 8, 7, 6, 5, 1]
[14, 13, 12, 11, 9, 8, 7, 6, 4, 1]
[14, 13, 12, 11, 9, 8, 7, 5, 4, 3]
[14, 13, 12, 11, 9, 8, 7, 5, 3, 1]
[14, 13, 12, 11, 9, 8, 7, 3, 2, 1]
[14, 13, 12, 11, 9, 8, 6, 5, 4, 3]
[14, 13, 12, 11, 9, 8, 6, 4, 3, 2]
[14, 13, 12, 11, 9, 8, 6, 3, 2, 1]
[14, 13, 12, 11, 9, 7, 6, 5, 4, 2]
[14, 13, 12, 11, 9, 7, 5, 4, 3, 1]
[14, 13, 12, 11, 9, 7, 5, 4, 2, 1]
[14, 13, 12, 11, 8, 7, 6, 4, 3, 2]
[14, 13, 12, 11, 8, 7, 6, 4, 2, 1]
[14, 13, 12, 11, 8, 6, 5, 4, 3, 1]
[14, 13, 12, 10, 9, 8, 7, 6, 4, 2]
[14, 13, 12, 10, 9, 8, 7, 6, 4, 1]
[14, 13, 12, 10, 9, 8, 7, 6, 2, 1]
[14, 13, 12, 10, 9, 8, 7, 5, 4, 2]
[14, 13, 12, 10, 9, 8, 7, 5, 2, 1]
[14, 13, 12, 10, 9, 8, 6, 5, 4, 1]
[14, 13, 12, 10, 9, 8, 6, 5, 3, 2]
[14, 13, 12, 10, 9, 8, 6, 4, 2, 1]
[14, 13, 12, 10, 9, 7, 6, 5, 4, 3]
[14, 13, 12, 10, 9, 7, 6, 5, 3, 1]
[14, 13, 12, 10, 8, 7, 6, 5, 4, 2]
[14, 13, 12, 10, 8, 7, 6, 5, 3, 1]
[14, 13, 12, 10, 8, 7, 5, 4, 3, 2]
[14, 13, 12, 10, 8, 6, 5, 4, 3, 1]
[14, 13, 12, 10, 7, 6, 5, 4, 3, 2]
[14, 13, 12, 9, 8, 7, 5, 4, 3, 2]
[14, 13, 12, 8, 7, 6, 5, 4, 3, 1]
[14, 13, 11, 10, 9, 8, 7, 6, 5, 3]
[14, 13, 11, 10, 9, 8, 7, 6, 4, 3]
[14, 13, 11, 10, 9, 8, 5, 4, 3, 1]
[14, 13, 11, 10, 9, 7, 6, 5, 4, 3]
[14, 13, 11, 10, 9, 7, 6, 4, 3, 2]
[14, 13, 11, 10, 9, 7, 6, 4, 3, 1]
[14, 13, 11, 10, 8, 7, 5, 4, 3, 2]
[14, 13, 11, 9, 8, 7, 6, 5, 4, 3]
[14, 13, 11, 9, 8, 7, 6, 5, 3, 2]
[14, 13, 11, 9, 8, 6, 5, 4, 3, 2]
[14, 12, 11, 10, 9, 8, 6, 5, 4, 2]
[14, 12, 11, 10, 9, 8, 5, 4, 3, 2]
[14, 12, 11, 10, 9, 7, 6, 5, 4, 2]


14 stages, 12 taps:  (5 sets)

[14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 2, 1]
[14, 13, 12, 11, 10, 9, 8, 7, 4, 3, 2, 1]
[14, 13, 12, 11, 10, 9, 8, 5, 4, 3, 2, 1]
[14, 13, 12, 11, 10, 8, 7, 6, 5, 4, 3, 2]
[14, 13, 12, 11, 10, 8, 7, 6, 5, 4, 3, 1]