Large Sets of t-Designs: LS[3](2,k,v)
Lehrstuhl II für Mathematik
Universität Bayreuth
Parameter sets are listed for v < 62 and t < k < v/2.
v denotes the row, an LS[3](2,k,v) exists if k appears in that row,
a '-' in the place of k indicates that no LS[3](2,k,v) exists,
a '?' in the place of k indicates that the existence of an LS[3](2,k,v) is unknown.
| 6 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - |
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| 7 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | |
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| 8 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - |
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| 9 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | |
|---|
| 10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | - |
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| 11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 3 | | 4 | | 5 | |
|---|
| 12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | 4 | | 5 | | 6 |
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| 13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | 5 | | 6 | |
|---|
| 14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | - | | 6 | | 7 |
|---|
| 15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | - | | - | | 7 | |
|---|
| 16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | - | | - | | - | | 8 |
|---|
| 17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | - | | - | | - | | - | |
|---|
| 18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | - | | - | | - | | - | | - |
|---|
| 19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | - | | - | | - | | - | | - | |
|---|
| 20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 3 | | 4 | | 5 | | 6 | | 7 | | 8 | | - | | - |
|---|
| 21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | 4 | | 5 | | 6 | | 7 | | 8 | | - | | - | |
|---|
| 22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | 5 | | 6 | | 7 | | 8 | | - | | - | | - |
|---|
| 23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | - | | 6 | | 7 | | 8 | | - | | - | | - | |
|---|
| 24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | - | | - | | 7 | | 8 | | - | | - | | - | | - |
|---|
| 25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | - | | - | | - | | 8 | | - | | - | | - | | - | |
|---|
| 26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - |
|---|
| 27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | |
|---|
| 28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - |
|---|
| 29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 3 | | 4 | | 5 | | 6 | | 7 | | 8 | | 9 | | 10 | | 11 | | ? | | ? | | ? | |
|---|
| 30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | 4 | | 5 | | 6 | | 7 | | 8 | | 9 | | 10 | | 11 | | ? | | ? | | ? | | ? |
|---|
| 31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | 5 | | 6 | | 7 | | 8 | | 9 | | 10 | | 11 | | 12 | | 13 | | 14 | | ? | |
|---|
| 32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | - | | 6 | | 7 | | 8 | | 9 | | 10 | | 11 | | 12 | | 13 | | 14 | | ? | | ? |
|---|
| 33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | - | | - | | 7 | | 8 | | 9 | | 10 | | 11 | | 12 | | 13 | | 14 | | ? | | ? | |
|---|
| 34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | - | | - | | - | | 8 | | 9 | | 10 | | 11 | | 12 | | 13 | | 14 | | 15 | | 16 | | 17 |
|---|
| 35 | | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | - | | - | | - | | - | | 9 | | 10 | | 11 | | 12 | | 13 | | 14 | | 15 | | 16 | | 17 | |
|---|
| 36 | | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | - | | - | | - | | - | | - | | 10 | | 11 | | 12 | | 13 | | 14 | | 15 | | 16 | | 17 | | 18 |
|---|
| 37 | | | | | | | | | | | | | | | | | | | | | | | | | - | | - | | - | | - | | - | | - | | - | | - | | 11 | | 12 | | 13 | | 14 | | 15 | | 16 | | 17 | | 18 | |
|---|
| 38 | | | | | | | | | | | | | | | | | | | | | | | | 3 | | 4 | | 5 | | 6 | | 7 | | 8 | | - | | - | | - | | 12 | | 13 | | 14 | | 15 | | 16 | | 17 | | 18 | | 19 |
|---|
| 39 | | | | | | | | | | | | | | | | | | | | | | | - | | 4 | | 5 | | 6 | | 7 | | 8 | | - | | - | | - | | - | | 13 | | 14 | | 15 | | 16 | | 17 | | 18 | | 19 | |
|---|
| 40 | | | | | | | | | | | | | | | | | | | | | | - | | - | | 5 | | 6 | | 7 | | 8 | | - | | - | | - | | - | | - | | 14 | | 15 | | 16 | | 17 | | 18 | | 19 | | 20 |
|---|
| 41 | | | | | | | | | | | | | | | | | | | | | - | | - | | - | | 6 | | 7 | | 8 | | - | | - | | - | | - | | - | | - | | 15 | | 16 | | 17 | | 18 | | 19 | | 20 | |
|---|
| 42 | | | | | | | | | | | | | | | | | | | | - | | - | | - | | - | | 7 | | 8 | | - | | - | | - | | - | | - | | - | | - | | 16 | | 17 | | 18 | | 19 | | 20 | | 21 |
|---|
| 43 | | | | | | | | | | | | | | | | | | | - | | - | | - | | - | | - | | 8 | | - | | - | | - | | - | | - | | - | | - | | - | | 17 | | 18 | | 19 | | 20 | | 21 | |
|---|
| 44 | | | | | | | | | | | | | | | | | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | 18 | | 19 | | 20 | | 21 | | 22 |
|---|
| 45 | | | | | | | | | | | | | | | | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | 19 | | 20 | | 21 | | 22 | |
|---|
| 46 | | | | | | | | | | | | | | | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | 20 | | 21 | | 22 | | 23 |
|---|
| 47 | | | | | | | | | | | | | | | 3 | | 4 | | 5 | | 6 | | 7 | | 8 | | - | | - | | - | | 12 | | 13 | | 14 | | 15 | | 16 | | 17 | | - | | - | | - | | 21 | | 22 | | 23 | |
|---|
| 48 | | | | | | | | | | | | | | - | | 4 | | 5 | | 6 | | 7 | | 8 | | - | | - | | - | | - | | 13 | | 14 | | 15 | | 16 | | 17 | | - | | - | | - | | - | | 22 | | 23 | | 24 |
|---|
| 49 | | | | | | | | | | | | | - | | - | | 5 | | 6 | | 7 | | 8 | | - | | - | | - | | - | | - | | 14 | | 15 | | 16 | | 17 | | - | | - | | - | | - | | - | | 23 | | 24 | |
|---|
| 50 | | | | | | | | | | | | - | | - | | - | | 6 | | 7 | | 8 | | - | | - | | - | | - | | - | | - | | 15 | | 16 | | 17 | | - | | - | | - | | - | | - | | - | | 24 | | 25 |
|---|
| 51 | | | | | | | | | | | - | | - | | - | | - | | 7 | | 8 | | - | | - | | - | | - | | - | | - | | - | | 16 | | 17 | | - | | - | | - | | - | | - | | - | | - | | 25 | |
|---|
| 52 | | | | | | | | | | - | | - | | - | | - | | - | | 8 | | - | | - | | - | | - | | - | | - | | - | | - | | 17 | | - | | - | | - | | - | | - | | - | | - | | - | | 26 |
|---|
| 53 | | | | | | | | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | |
|---|
| 54 | | | | | | | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - |
|---|
| 55 | | | | | | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | | - | |
|---|
| 56 | | | | | | 3 | | 4 | | 5 | | 6 | | 7 | | 8 | | 9 | | 10 | | 11 | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | - | | - |
|---|
| 57 | | | | | - | | 4 | | 5 | | 6 | | 7 | | 8 | | 9 | | 10 | | 11 | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | - | | - | |
|---|
| 58 | | | | - | | - | | 5 | | 6 | | 7 | | 8 | | 9 | | 10 | | 11 | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | ? | | - | | - | | - |
|---|
| 59 | | | - | | - | | - | | 6 | | 7 | | 8 | | 9 | | 10 | | 11 | | 12 | | 13 | | 14 | | 15 | | 16 | | 17 | | 18 | | 19 | | 20 | | 21 | | 22 | | 23 | | 24 | | 25 | | 26 | | - | | - | | - | |
|---|
| 60 | | - | | - | | - | | - | | 7 | | 8 | | 9 | | 10 | | 11 | | 12 | | 13 | | 14 | | 15 | | 16 | | 17 | | 18 | | 19 | | 20 | | 21 | | 22 | | 23 | | 24 | | 25 | | 26 | | - | | - | | - | | - |
|---|
| 61 | | | - | | - | | - | | - | | 8 | | 9 | | 10 | | 11 | | 12 | | 13 | | 14 | | 15 | | 16 | | 17 | | 18 | | 19 | | 20 | | 21 | | 22 | | 23 | | 24 | | 25 | | 26 | | - | | - | | - | | - | |
|---|