(66,26,10) block plan
The (66,26,10) block diagram is a special symmetrical block diagram . In order to be able to construct it, this combinatorial problem had to be solved: an empty 66 × 66 matrix was filled with ones in such a way that each row of the matrix contains exactly 26 ones and any two rows have exactly 10 ones in the same column (not more and not less). That sounds relatively simple, but it is not trivial to solve. There are only certain combinations of parameters (like here v = 66, k = 26, λ = 10) for which such a construction is feasible. The smallest of these (v, k, λ) are listed in this overview .
properties
This symmetrical block diagram has the parameters v = 66, k = 26, λ = 10 and thus the following properties:
- It consists of 66 blocks and 66 points.
- Each block contains exactly 26 points.
- Every 2 blocks intersect in exactly 10 points.
- Each point lies on exactly 26 blocks.
- Each 2 points are connected by exactly 10 blocks.
Existence and characterization
There are at least 588 non-isomorphic 2- (66,26,10) block plans. Three of these solutions are:
- Solution 1 with the signature 55x65, 11x75. It contains 110 ovals of the 3rd order.
- Solution 2 ( dual to solution 3) with the signature 25 x 3, 5 x 5, 25 x 6, 10 x 10, 1 x 100. It contains 85 ovals of the 3rd order.
- Solution 3 ( dual to solution 2) with the signature 5 x 5, 25 x 9, 5 x 10, 25 x 15, 6 x 25. It contains 60 ovals of the 3rd order.
List of blocks
All the blocks of this block plan are listed here; See this illustration to understand this list
- Solution 1
1 22 23 24 25 26 32 33 34 35 36 42 43 44 45 46 47 48 49 50 51 62 63 64 65 66 2 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 47 48 49 50 51 57 58 59 60 61 3 12 13 14 15 16 27 28 29 30 31 47 48 49 50 51 52 53 54 55 56 62 63 64 65 66 4 12 13 14 15 16 17 18 19 20 21 42 43 44 45 46 47 48 49 50 51 57 58 59 60 61 5 17 18 19 20 21 22 23 24 25 26 37 38 39 40 41 47 48 49 50 51 52 53 54 55 56 6 17 18 19 20 21 27 28 29 30 31 37 38 39 40 41 42 43 44 45 46 62 63 64 65 66 7 12 13 14 15 16 22 23 24 25 26 37 38 39 40 41 57 58 59 60 61 62 63 64 65 66 8 17 18 19 20 21 32 33 34 35 36 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 9 22 23 24 25 26 27 28 29 30 31 42 43 44 45 46 52 53 54 55 56 57 58 59 60 61 10 12 13 14 15 16 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 52 53 54 55 56 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3 4 7 10 11 12 19 20 24 25 28 31 33 36 39 40 43 46 49 50 54 55 58 61 63 66 3 4 7 10 11 13 20 21 25 26 27 29 32 34 40 41 42 44 50 51 55 56 57 59 62 64 3 4 7 10 11 14 17 21 22 26 28 30 33 35 37 41 43 45 47 51 52 56 58 60 63 65 3 4 7 10 11 15 17 18 22 23 29 31 34 36 37 38 44 46 47 48 52 53 59 61 64 66 3 4 7 10 11 16 18 19 23 24 27 30 32 35 38 39 42 45 48 49 53 54 57 60 62 65 4 5 6 8 11 13 16 17 24 25 29 30 33 36 38 41 44 45 48 51 54 55 59 60 63 66 4 5 6 8 11 12 14 18 25 26 30 31 32 34 37 39 45 46 47 49 55 56 60 61 62 64 4 5 6 8 11 13 15 19 22 26 27 31 33 35 38 40 42 46 48 50 52 56 57 61 63 65 4 5 6 8 11 14 16 20 22 23 27 28 34 36 39 41 42 43 49 51 52 53 57 58 64 66 4 5 6 8 11 12 15 21 23 24 28 29 32 35 37 40 43 44 47 50 53 54 58 59 62 65 1 5 7 9 11 13 16 18 21 22 29 30 34 35 39 40 43 46 49 50 53 56 59 60 63 66 1 5 7 9 11 12 14 17 19 23 30 31 35 36 40 41 42 44 50 51 52 54 60 61 62 64 1 5 7 9 11 13 15 18 20 24 27 31 32 36 37 41 43 45 47 51 53 55 57 61 63 65 1 5 7 9 11 14 16 19 21 25 27 28 32 33 37 38 44 46 47 48 54 56 57 58 64 66 1 5 7 9 11 12 15 17 20 26 28 29 33 34 38 39 42 45 48 49 52 55 58 59 62 65 2 3 6 9 11 14 15 18 21 23 26 27 34 35 39 40 44 45 48 51 54 55 58 61 63 66 2 3 6 9 11 15 16 17 19 22 24 28 35 36 40 41 45 46 47 49 55 56 57 59 62 64 2 3 6 9 11 12 16 18 20 23 25 29 32 36 37 41 42 46 48 50 52 56 58 60 63 65 2 3 6 9 11 12 13 19 21 24 26 30 32 33 37 38 42 43 49 51 52 53 59 61 64 66 2 3 6 9 11 13 14 17 20 22 25 31 33 34 38 39 43 44 47 50 53 54 57 60 62 65 1 2 8 10 11 14 15 19 20 23 26 28 31 32 38 41 44 45 49 50 53 56 59 60 63 66 1 2 8 10 11 15 16 20 21 22 24 27 29 33 37 39 45 46 50 51 52 54 60 61 62 64 1 2 8 10 11 12 16 17 21 23 25 28 30 34 38 40 42 46 47 51 53 55 57 61 63 65 1 2 8 10 11 12 13 17 18 24 26 29 31 35 39 41 42 43 47 48 54 56 57 58 64 66 1 2 8 10 11 13 14 18 19 22 25 27 30 36 37 40 43 44 48 49 52 55 58 59 62 65 2 5 6 7 10 13 16 19 20 23 26 28 31 34 35 37 43 46 48 51 54 55 59 60 64 65 2 5 6 7 10 12 14 20 21 22 24 27 29 35 36 38 42 44 47 49 55 56 60 61 65 66 2 5 6 7 10 13 15 17 21 23 25 28 30 32 36 39 43 45 48 50 52 56 57 61 62 66 2 5 6 7 10 14 16 17 18 24 26 29 31 32 33 40 44 46 49 51 52 53 57 58 62 63 2 5 6 7 10 12 15 18 19 22 25 27 30 33 34 41 42 45 47 50 53 54 58 59 63 64 1 4 6 9 10 14 15 18 21 24 25 28 31 33 36 39 40 42 48 51 53 56 59 60 64 65 1 4 6 9 10 15 16 17 19 25 26 27 29 32 34 40 41 43 47 49 52 54 60 61 65 66 1 4 6 9 10 12 16 18 20 22 26 28 30 33 35 37 41 44 48 50 53 55 57 61 62 66 1 4 6 9 10 12 13 19 21 22 23 29 31 34 36 37 38 45 49 51 54 56 57 58 62 63 1 4 6 9 10 13 14 17 20 23 24 27 30 32 35 38 39 46 47 50 52 55 58 59 63 64 1 2 3 4 5 13 16 19 20 23 26 29 30 33 36 39 40 44 45 47 53 56 58 61 64 65 1 2 3 4 5 12 14 20 21 22 24 30 31 32 34 40 41 45 46 48 52 54 57 59 65 66 1 2 3 4 5 13 15 17 21 23 25 27 31 33 35 37 41 42 46 49 53 55 58 60 62 66 1 2 3 4 5 14 16 17 18 24 26 27 28 34 36 37 38 42 43 50 54 56 59 61 62 63 1 2 3 4 5 12 15 18 19 22 25 28 29 32 35 38 39 43 44 51 52 55 57 60 63 64 3 5 8 9 10 13 16 18 21 24 25 28 31 34 35 38 41 44 45 49 50 52 58 61 64 65 3 5 8 9 10 12 14 17 19 25 26 27 29 35 36 37 39 45 46 50 51 53 57 59 65 66 3 5 8 9 10 13 15 18 20 22 26 28 30 32 36 38 40 42 46 47 51 54 58 60 62 66 3 5 8 9 10 14 16 19 21 22 23 29 31 32 33 39 41 42 43 47 48 55 59 61 62 63 3 5 8 9 10 12 15 17 20 23 24 27 30 33 34 37 40 43 44 48 49 56 57 60 63 64 2 4 7 8 9 14 15 18 21 23 26 29 30 33 36 38 41 43 46 49 50 54 55 57 64 65 2 4 7 8 9 15 16 17 19 22 24 30 31 32 34 37 39 42 44 50 51 55 56 58 65 66 2 4 7 8 9 12 16 18 20 23 25 27 31 33 35 38 40 43 45 47 51 52 56 59 62 66 2 4 7 8 9 12 13 19 21 24 26 27 28 34 36 39 41 44 46 47 48 52 53 60 62 63 2 4 7 8 9 13 14 17 20 22 25 28 29 32 35 37 40 42 45 48 49 53 54 61 63 64 1 3 6 7 8 14 15 19 20 24 25 29 30 34 35 38 41 43 46 48 51 53 56 58 61 62 1 3 6 7 8 15 16 20 21 25 26 30 31 35 36 37 39 42 44 47 49 52 54 57 59 63 1 3 6 7 8 12 16 17 21 22 26 27 31 32 36 38 40 43 45 48 50 53 55 58 60 64 1 3 6 7 8 12 13 17 18 22 23 27 28 32 33 39 41 44 46 49 51 54 56 59 61 65 1 3 6 7 8 13 14 18 19 23 24 28 29 33 34 37 40 42 45 47 50 52 55 57 60 66
- Solution 2
1 22 23 24 25 26 32 33 34 35 36 42 43 44 45 46 47 48 49 50 51 62 63 64 65 66 2 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 47 48 49 50 51 57 58 59 60 61 3 12 13 14 15 16 27 28 29 30 31 47 48 49 50 51 52 53 54 55 56 62 63 64 65 66 4 12 13 14 15 16 17 18 19 20 21 42 43 44 45 46 47 48 49 50 51 57 58 59 60 61 5 17 18 19 20 21 22 23 24 25 26 37 38 39 40 41 47 48 49 50 51 52 53 54 55 56 6 17 18 19 20 21 27 28 29 30 31 37 38 39 40 41 42 43 44 45 46 62 63 64 65 66 7 12 13 14 15 16 22 23 24 25 26 37 38 39 40 41 57 58 59 60 61 62 63 64 65 66 8 17 18 19 20 21 32 33 34 35 36 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 9 22 23 24 25 26 27 28 29 30 31 42 43 44 45 46 52 53 54 55 56 57 58 59 60 61 10 12 13 14 15 16 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 52 53 54 55 56 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3 4 7 10 11 12 18 20 24 26 29 31 33 35 37 38 44 45 49 50 52 53 58 59 63 66 3 4 7 10 11 13 19 21 22 25 27 30 34 36 38 39 45 46 50 51 53 54 59 60 62 64 3 4 7 10 11 14 17 20 23 26 28 31 32 35 39 40 42 46 47 51 54 55 60 61 63 65 3 4 7 10 11 15 18 21 22 24 27 29 33 36 40 41 42 43 47 48 55 56 57 61 64 66 3 4 7 10 11 16 17 19 23 25 28 30 32 34 37 41 43 44 48 49 52 56 57 58 62 65 4 5 6 8 11 13 15 17 23 25 29 31 34 36 38 39 42 43 49 50 54 55 57 58 63 66 4 5 6 8 11 14 16 18 24 26 27 30 32 35 39 40 43 44 50 51 55 56 58 59 62 64 4 5 6 8 11 12 15 19 22 25 28 31 33 36 40 41 44 45 47 51 52 56 59 60 63 65 4 5 6 8 11 13 16 20 23 26 27 29 32 34 37 41 45 46 47 48 52 53 60 61 64 66 4 5 6 8 11 12 14 21 22 24 28 30 33 35 37 38 42 46 48 49 53 54 57 61 62 65 1 5 7 9 11 14 16 18 20 22 28 30 34 36 37 38 43 44 47 48 54 55 59 60 63 66 1 5 7 9 11 12 15 19 21 23 29 31 32 35 38 39 44 45 48 49 55 56 60 61 62 64 1 5 7 9 11 13 16 17 20 24 27 30 33 36 39 40 45 46 49 50 52 56 57 61 63 65 1 5 7 9 11 12 14 18 21 25 28 31 32 34 40 41 42 46 50 51 52 53 57 58 64 66 1 5 7 9 11 13 15 17 19 26 27 29 33 35 37 41 42 43 47 51 53 54 58 59 62 65 2 3 6 9 11 14 16 19 21 23 25 27 33 35 39 40 42 43 48 49 52 53 59 60 63 66 2 3 6 9 11 12 15 17 20 24 26 28 34 36 40 41 43 44 49 50 53 54 60 61 62 64 2 3 6 9 11 13 16 18 21 22 25 29 32 35 37 41 44 45 50 51 54 55 57 61 63 65 2 3 6 9 11 12 14 17 19 23 26 30 33 36 37 38 45 46 47 51 55 56 57 58 64 66 2 3 6 9 11 13 15 18 20 22 24 31 32 34 38 39 42 46 47 48 52 56 58 59 62 65 1 2 8 10 11 13 15 19 21 24 26 28 30 32 39 40 44 45 47 48 53 54 57 58 63 66 1 2 8 10 11 14 16 17 20 22 25 29 31 33 40 41 45 46 48 49 54 55 58 59 62 64 1 2 8 10 11 12 15 18 21 23 26 27 30 34 37 41 42 46 49 50 55 56 59 60 63 65 1 2 8 10 11 13 16 17 19 22 24 28 31 35 37 38 42 43 50 51 52 56 60 61 64 66 1 2 8 10 11 12 14 18 20 23 25 27 29 36 38 39 43 44 47 51 52 53 57 61 62 65 2 5 6 7 10 14 15 17 19 24 25 27 31 32 36 37 44 46 48 50 53 55 59 61 65 66 2 5 6 7 10 15 16 18 20 25 26 27 28 32 33 38 42 45 49 51 54 56 57 60 62 66 2 5 6 7 10 12 16 19 21 22 26 28 29 33 34 39 43 46 47 50 52 55 58 61 62 63 2 5 6 7 10 12 13 17 20 22 23 29 30 34 35 40 42 44 48 51 53 56 57 59 63 64 2 5 6 7 10 13 14 18 21 23 24 30 31 35 36 41 43 45 47 49 52 54 58 60 64 65 1 4 6 9 10 12 16 19 20 22 24 29 30 32 36 39 41 42 49 51 53 55 58 60 65 66 1 4 6 9 10 12 13 20 21 23 25 30 31 32 33 37 40 43 47 50 54 56 59 61 62 66 1 4 6 9 10 13 14 17 21 24 26 27 31 33 34 38 41 44 48 51 52 55 57 60 62 63 1 4 6 9 10 14 15 17 18 22 25 27 28 34 35 37 39 45 47 49 53 56 58 61 63 64 1 4 6 9 10 15 16 18 19 23 26 28 29 35 36 38 40 46 48 50 52 54 57 59 64 65 1 2 3 4 5 12 16 17 21 24 25 27 29 34 35 38 40 44 46 47 54 56 58 60 65 66 1 2 3 4 5 12 13 17 18 25 26 28 30 35 36 39 41 42 45 48 52 55 59 61 62 66 1 2 3 4 5 13 14 18 19 22 26 29 31 32 36 37 40 43 46 49 53 56 57 60 62 63 1 2 3 4 5 14 15 19 20 22 23 27 30 32 33 38 41 42 44 50 52 54 58 61 63 64 1 2 3 4 5 15 16 20 21 23 24 28 31 33 34 37 39 43 45 51 53 55 57 59 64 65 3 5 8 9 10 14 15 17 21 22 26 29 30 32 34 38 40 43 45 49 51 52 59 61 65 66 3 5 8 9 10 15 16 17 18 22 23 30 31 33 35 39 41 44 46 47 50 53 57 60 62 66 3 5 8 9 10 12 16 18 19 23 24 27 31 34 36 37 40 42 45 48 51 54 58 61 62 63 3 5 8 9 10 12 13 19 20 24 25 27 28 32 35 38 41 43 46 47 49 55 57 59 63 64 3 5 8 9 10 13 14 20 21 25 26 28 29 33 36 37 39 42 44 48 50 56 58 60 64 65 2 4 7 8 9 12 14 19 20 22 26 27 31 34 35 39 41 43 45 48 50 54 56 57 65 66 2 4 7 8 9 13 15 20 21 22 23 27 28 35 36 37 40 44 46 49 51 52 55 58 62 66 2 4 7 8 9 14 16 17 21 23 24 28 29 32 36 38 41 42 45 47 50 53 56 59 62 63 2 4 7 8 9 12 15 17 18 24 25 29 30 32 33 37 39 43 46 48 51 52 54 60 63 64 2 4 7 8 9 13 16 18 19 25 26 30 31 33 34 38 40 42 44 47 49 53 55 61 64 65 1 3 6 7 8 14 15 19 20 24 25 29 30 34 35 37 40 42 45 47 50 52 55 57 60 62 1 3 6 7 8 15 16 20 21 25 26 30 31 35 36 38 41 43 46 48 51 53 56 58 61 63 1 3 6 7 8 12 16 17 21 22 26 27 31 32 36 37 39 42 44 47 49 52 54 57 59 64 1 3 6 7 8 12 13 17 18 22 23 27 28 32 33 38 40 43 45 48 50 53 55 58 60 65 1 3 6 7 8 13 14 18 19 23 24 28 29 33 34 39 41 44 46 49 51 54 56 59 61 66
- Solution 3
1 22 23 24 25 26 32 33 34 35 36 42 43 44 45 46 47 48 49 50 51 62 63 64 65 66 2 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 47 48 49 50 51 57 58 59 60 61 3 12 13 14 15 16 27 28 29 30 31 47 48 49 50 51 52 53 54 55 56 62 63 64 65 66 4 12 13 14 15 16 17 18 19 20 21 42 43 44 45 46 47 48 49 50 51 57 58 59 60 61 5 17 18 19 20 21 22 23 24 25 26 37 38 39 40 41 47 48 49 50 51 52 53 54 55 56 6 17 18 19 20 21 27 28 29 30 31 37 38 39 40 41 42 43 44 45 46 62 63 64 65 66 7 12 13 14 15 16 22 23 24 25 26 37 38 39 40 41 57 58 59 60 61 62 63 64 65 66 8 17 18 19 20 21 32 33 34 35 36 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 9 22 23 24 25 26 27 28 29 30 31 42 43 44 45 46 52 53 54 55 56 57 58 59 60 61 10 12 13 14 15 16 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 52 53 54 55 56 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3 4 7 10 11 12 19 21 23 25 28 30 34 36 39 40 42 43 47 48 54 55 57 60 64 65 3 4 7 10 11 13 17 20 24 26 29 31 32 35 40 41 43 44 48 49 55 56 58 61 65 66 3 4 7 10 11 14 18 21 22 25 27 30 33 36 37 41 44 45 49 50 52 56 57 59 62 66 3 4 7 10 11 15 17 19 23 26 28 31 32 34 37 38 45 46 50 51 52 53 58 60 62 63 3 4 7 10 11 16 18 20 22 24 27 29 33 35 38 39 42 46 47 51 53 54 59 61 63 64 4 5 6 8 11 14 16 17 24 26 28 30 33 35 37 40 44 45 47 48 52 53 59 60 64 65 4 5 6 8 11 12 15 18 22 25 29 31 34 36 38 41 45 46 48 49 53 54 60 61 65 66 4 5 6 8 11 13 16 19 23 26 27 30 32 35 37 39 42 46 49 50 54 55 57 61 62 66 4 5 6 8 11 12 14 20 22 24 28 31 33 36 38 40 42 43 50 51 55 56 57 58 62 63 4 5 6 8 11 13 15 21 23 25 27 29 32 34 39 41 43 44 47 51 52 56 58 59 63 64 1 5 7 9 11 13 15 19 21 22 29 31 33 35 39 40 42 45 49 50 52 53 57 58 64 65 1 5 7 9 11 14 16 17 20 23 27 30 34 36 40 41 43 46 50 51 53 54 58 59 65 66 1 5 7 9 11 12 15 18 21 24 28 31 32 35 37 41 42 44 47 51 54 55 59 60 62 66 1 5 7 9 11 13 16 17 19 25 27 29 33 36 37 38 43 45 47 48 55 56 60 61 62 63 1 5 7 9 11 12 14 18 20 26 28 30 32 34 38 39 44 46 48 49 52 56 57 61 63 64 2 3 6 9 11 13 15 18 20 24 26 27 34 36 37 38 44 45 47 50 54 55 57 58 64 65 2 3 6 9 11 14 16 19 21 22 25 28 32 35 38 39 45 46 48 51 55 56 58 59 65 66 2 3 6 9 11 12 15 17 20 23 26 29 33 36 39 40 42 46 47 49 52 56 59 60 62 66 2 3 6 9 11 13 16 18 21 22 24 30 32 34 40 41 42 43 48 50 52 53 60 61 62 63 2 3 6 9 11 12 14 17 19 23 25 31 33 35 37 41 43 44 49 51 53 54 57 61 63 64 1 2 8 10 11 14 16 18 20 23 25 29 31 32 37 38 42 43 49 50 52 55 59 60 64 65 1 2 8 10 11 12 15 19 21 24 26 27 30 33 38 39 43 44 50 51 53 56 60 61 65 66 1 2 8 10 11 13 16 17 20 22 25 28 31 34 39 40 44 45 47 51 52 54 57 61 62 66 1 2 8 10 11 12 14 18 21 23 26 27 29 35 40 41 45 46 47 48 53 55 57 58 62 63 1 2 8 10 11 13 15 17 19 22 24 28 30 36 37 41 42 46 48 49 54 56 58 59 63 64 2 5 6 7 10 12 16 20 21 22 26 29 30 34 35 37 43 45 49 51 54 56 58 60 62 64 2 5 6 7 10 12 13 17 21 22 23 30 31 35 36 38 44 46 47 50 52 55 59 61 63 65 2 5 6 7 10 13 14 17 18 23 24 27 31 32 36 39 42 45 48 51 53 56 57 60 64 66 2 5 6 7 10 14 15 18 19 24 25 27 28 32 33 40 43 46 47 49 52 54 58 61 62 65 2 5 6 7 10 15 16 19 20 25 26 28 29 33 34 41 42 44 48 50 53 55 57 59 63 66 1 4 6 9 10 14 15 17 21 25 26 27 31 34 35 38 40 42 48 50 54 56 59 61 62 64 1 4 6 9 10 15 16 17 18 22 26 27 28 35 36 39 41 43 49 51 52 55 57 60 63 65 1 4 6 9 10 12 16 18 19 22 23 28 29 32 36 37 40 44 47 50 53 56 58 61 64 66 1 4 6 9 10 12 13 19 20 23 24 29 30 32 33 38 41 45 48 51 52 54 57 59 62 65 1 4 6 9 10 13 14 20 21 24 25 30 31 33 34 37 39 46 47 49 53 55 58 60 63 66 1 2 3 4 5 14 15 19 20 22 26 30 31 32 36 39 41 43 45 47 53 55 59 61 62 64 1 2 3 4 5 15 16 20 21 22 23 27 31 32 33 37 40 44 46 48 54 56 57 60 63 65 1 2 3 4 5 12 16 17 21 23 24 27 28 33 34 38 41 42 45 49 52 55 58 61 64 66 1 2 3 4 5 12 13 17 18 24 25 28 29 34 35 37 39 43 46 50 53 56 57 59 62 65 1 2 3 4 5 13 14 18 19 25 26 29 30 35 36 38 40 42 44 51 52 54 58 60 63 66 3 5 8 9 10 12 16 19 20 24 25 27 31 35 36 39 41 44 46 48 50 52 58 60 62 64 3 5 8 9 10 12 13 20 21 25 26 27 28 32 36 37 40 42 45 49 51 53 59 61 63 65 3 5 8 9 10 13 14 17 21 22 26 28 29 32 33 38 41 43 46 47 50 54 57 60 64 66 3 5 8 9 10 14 15 17 18 22 23 29 30 33 34 37 39 42 44 48 51 55 58 61 62 65 3 5 8 9 10 15 16 18 19 23 24 30 31 34 35 38 40 43 45 47 49 56 57 59 63 66 2 4 7 8 9 15 16 17 21 24 25 29 30 32 36 38 40 44 46 49 51 53 55 57 62 64 2 4 7 8 9 12 16 17 18 25 26 30 31 32 33 39 41 42 45 47 50 54 56 58 63 65 2 4 7 8 9 12 13 18 19 22 26 27 31 33 34 37 40 43 46 48 51 52 55 59 64 66 2 4 7 8 9 13 14 19 20 22 23 27 28 34 35 38 41 42 44 47 49 53 56 60 62 65 2 4 7 8 9 14 15 20 21 23 24 28 29 35 36 37 39 43 45 48 50 52 54 61 63 66 1 3 6 7 8 13 16 18 21 23 26 28 31 33 36 38 39 43 44 48 49 53 54 58 59 62 1 3 6 7 8 12 14 17 19 22 24 27 29 32 34 39 40 44 45 49 50 54 55 59 60 63 1 3 6 7 8 13 15 18 20 23 25 28 30 33 35 40 41 45 46 50 51 55 56 60 61 64 1 3 6 7 8 14 16 19 21 24 26 29 31 34 36 37 41 42 46 47 51 52 56 57 61 65 1 3 6 7 8 12 15 17 20 22 25 27 30 32 35 37 38 42 43 47 48 52 53 57 58 66
oval
An oval of the block plan is a set of its points, no three of which are on a block. Here is an example of a maximum order oval for each solution to this block diagram:
- Solution 1
1 2 6
- Solution 2
1 2 6
- Solution 3
1 2 6
literature
- Thomas Beth , Dieter Jungnickel , Hanfried Lenz : Design Theory . 1st edition. BI Wissenschaftsverlag, Mannheim / Vienna / Zurich 1985, ISBN 3-411-01675-2 .
- Albrecht Beutelspacher : Introduction to Finite Geometry. Volume 1: Block Plans . BI Wissenschaftsverlag, Mannheim / Vienna / Zurich 1982, ISBN 3-411-01632-9 .
Web links
Individual evidence
- ↑ Tran van Trung : The existence of symmetric block designs with parameters (41,16,6) and (66,26,10). In: Journal of Combinatorial Theory, Series A. Vol. 33, No. 2, 1982, pp. 201-204, doi : 10.1016 / 0097-3165 (82) 90008-5 .
- ^ Rudolf Mathon, Alexander Rosa : 2- (ν, κ, λ) Designs of Small Order. In: Charles J. Colbourn , Jeffrey H. Dinitz (Eds.): Handbook of Combinatorial Designs. 2nd edition. Chapman and Hall / CRC, Boca Raton FL et al. 2007, ISBN 978-1-4200-1054-1 , pp. 25-57.