A single Berge k-move is denoted as { j i }, in which case, the pieces in the positions
i,i+1,...,i+k-1 are moved to the vacant holes j,j+1,...,j+k-1.  Successive moves are concatenated
as { j i } U { l k }, which means perform { j i } followed by { l k }. Often a move fills an
empty hole created as an effect of the previous move, the resulting notation { j k } U { k i }
is abbreviated as { j k i }, and is extended to more than two such moves as well.

S[10, 8]: { 11 2 } U { 19 10 } U { -7 18 } U { -15 -6 } U { 18 -14 } U { -23 19 } U { 10 -22 } U { 2 11 } U { -6 3 } U { -22 -5 } U { -14 -23 }
S[11, 8]: { 12 1 10 2 } U { -7 12 } U { -15 -6 } U { -23 -14 } U { 2 -22 } U { -6 4 } U { -22 -4 } U { -14 -23 }
S[12, 8]: { 13 3 } U { -7 12 } U { -15 -5 } U { 12 -14 } U { -23 13 } U { 3 -22 } U { -5 5 } U { -22 -3 } U { -14 -23 }
S[13, 8]: { 14 1 11 3 13 5 14 } U { -7 4 -4 6 }
S[14, 8]: { 15 4 14 3 } U { -7 15 } U { 3 -5 6 -4 4 -7 }
S[15, 8]: { 16 5 15 4 12 } U { 24 2 21 3 24 } U { 12 1 }
S[16, 8]: { 17 2 12 1 16 6 17 2 13 4 17 }
S[17, 8]: { 18 5 17 7 16 3 12 1 15 5 18 }
S[18, 8]: { 19 2 } U { 27 15 } U { 2 26 4 } U { 15 25 13 } U { 4 24 } U { 13 1 } U { 24 10 27 }
S[19, 8]: { 20 3 14 4 15 5 19 2 17 4 16 1 }
S[20, 8]: { 21 7 20 8 18 3 13 4 20 8 18 1 }
S[21, 8]: { 22 9 } U { -7 17 } U { 9 -6 7 } U { 17 -3 } U { 7 21 } U { -3 10 } U { 21 -7 } U { 10 19 6 22 }
S[22, 8]: { 23 5 18 4 20 9 22 5 16 2 17 6 23 }
S[23, 8]: { 24 13 4 20 11 2 16 4 21 9 22 6 24 }
S[24, 8]: { 25 2 23 3 22 13 25 6 23 12 3 19 10 25 }
S[25, 8]: { 26 3 12 24 1 } U { 34 22 10 19 31 21 33 15 26 9 }
S[26, 8]: { 27 2 13 24 4 20 3 19 7 26 10 20 4 25 1 }
S[27, 8]: { 28 17 2 } U { 36 15 33 18 31 13 29 11 24 36 } U { 2 23 9 28 }
S[28, 8]: { 29 4 13 } U { 37 25 2 } U { 13 22 34 15 36 } U { 2 18 6 20 } U { 36 9 } U { 20 32 1 }
S[29, 8]: { 30 19 2 26 4 22 8 25 3 12 29 15 27 8 20 1 }
S[30, 8]: { 31 2 15 } U { -7 6 26 -5 30 } U { 15 -6 17 5 21 -2 19 3 -7 } U { 30 1 }
S[31, 8]: { 32 5 20 4 22 7 31 2 26 11 27 12 23 5 26 11 32 }
S[32, 8]: { 33 2 11 24 } U { -7 9 } U { 24 -4 } U { 9 26 } U { -4 14 } U { 26 2 32 } U { 14 0 } U { 32 21 30 19 } U { 0 33 } U { 19 3 25 }
S[33, 8]: { 34 1 24 11 31 18 33 13 29 6 19 4 25 2 32 14 30 1 }
S[34, 8]: { 35 16 25 6 30 2 28 9 34 6 18 3 15 24 8 18 4 35 }
S[35, 8]: { 36 3 12 21 35 2 24 8 30 17 34 3 24 12 27 8 29 15 36 }
S[36, 8]: { 37 26 3 14 30 7 36 2 25 9 32 16 27 4 31 9 28 10 37 }
S[37, 8]: { 38 3 12 21 7 36 4 30 9 35 5 16 37 12 28 10 34 7 27 1 }
S[38, 8]: { 39 12 3 30 21 5 26 2 28 37 16 32 11 36 23 14 27 12 38 1 }
S[39, 8]: { 40 1 29 16 36 18 7 25 12 39 16 2 37 18 34 6 27 11 33 15 40 }
S[40, 8]: { 41 2 11 32 21 5 14 25 34 3 40 10 29 8 24 6 20 30 11 39 1 }
S[41, 8]: { 42 1 20 11 32 4 25 36 27 2 41 14 23 7 34 4 36 25 40 22 11 42 }
S[42, 8]: { 43 2 21 12 33 5 26 37 28 3 42 15 24 8 35 5 37 26 41 23 12 43 }
S[43, 8]: { 44 1 10 19 3 35 15 40 22 9 26 42 12 2 37 17 30 15 43 33 14 37 1 }
S[44, 8]: { 45 2 11 22 35 5 38 15 31 43 24 3 30 40 17 8 35 19 10 34 15 44 1 }
S[45, 8]: { 46 1 10 19 28 37 13 44 31 22 3 27 8 23 38 2 18 9 45 3 12 22 5 46 }
S[46, 8]: { 47 2 11 20 29 38 14 45 32 23 4 28 9 24 39 3 19 10 46 4 13 23 6 47 }
S[47, 8]: { 48 1 10 19 3 37 15 42 8 38 47 31 6 24 4 43 22 38 11 2 26 7 18 44 1 }
S[48, 8]: { 49 2 11 20 4 17 33 10 37 24 42 17 46 3 48 10 26 6 19 45 10 36 24 46 1 }
S[49, 8]: { 50 1 10 19 3 14 30 9 20 5 40 2 47 25 49 4 21 36 45 24 34 19 48 35 10 50 }
S[50, 8]: { 51 2 11 20 4 15 31 10 21 6 41 3 48 26 50 5 22 37 46 25 35 20 49 36 11 51 }