C-39

Evidence

Explicit block file attached (one block per line, 1-indexed, sorted). Coverage verified exhaustively (0 uncovered t-subsets).

Prior best 38 (LJCR v1.2 and coveringrepository.com).
Method: weighted tabu local search with single-point swaps from random blocks.
All 54,740 triples covered.
Prior-art disclosure: irsi.ai/tables.html also recently posted a 37-block (70,25,3) certificate. This design was found independently and is non-isomorphic to theirs: point-degree profile {12:6, 13:56, 14:4, 16:2, 18:1, 19:1} vs theirs {12:6, 13:53, 14:5, 15:4, 17:2}. Priority for the 37-block bound may belong to irsi.ai; this claim is offered as an independent, non-isomorphic certificate.
Author: Caleb Ashton.
SHA-256 of the block file: 8e46960ab4f6225651916c523a88b2d7bf850656cedefcc9f70f7c6fb77325e4.
LJCR entry: https://ljcr.dmgordon.org/cover/show_cover.php?v=70&k=25&t=3

All blocks (one per line):
1 5 7 12 17 18 21 24 29 30 31 32 35 41 45 46 51 52 60 61 62 63 64 67 68
4 7 11 13 16 18 19 23 25 28 29 31 32 34 35 37 39 41 47 48 58 59 64 67 68
6 10 13 15 19 25 27 33 34 36 37 38 40 43 49 50 53 55 56 57 62 64 65 66 67
3 5 8 13 18 19 20 21 24 25 27 28 29 30 36 38 39 44 45 53 58 59 60 65 67
1 8 13 14 16 21 24 27 31 32 33 38 45 50 54 56 59 60 62 64 65 66 68 69 70
1 2 3 4 7 10 15 17 23 26 28 35 39 40 41 42 43 44 46 47 49 52 61 64 67
4 8 16 17 18 20 22 23 29 34 36 37 40 43 46 47 51 52 53 61 62 63 67 69 70
1 2 5 6 13 14 16 20 26 27 28 30 38 39 40 42 43 51 54 55 57 58 63 65 67
1 2 9 11 12 21 24 26 28 31 32 34 36 37 39 40 42 43 45 48 53 60 62 67 68
6 9 10 13 14 15 17 18 19 25 28 29 39 46 49 51 52 54 55 57 59 61 62 63 67
1 2 8 12 13 18 19 20 22 25 26 28 29 33 39 40 42 43 50 56 59 66 67 69 70
2 5 6 7 8 10 11 12 13 15 16 19 25 26 30 35 41 42 48 49 55 57 62 69 70
1 6 7 8 9 13 17 20 33 34 35 37 41 46 50 52 55 56 57 58 59 61 66 69 70
4 5 7 8 9 12 13 20 22 23 27 28 30 33 35 38 39 41 47 50 56 62 64 65 66
5 8 10 11 15 17 20 27 28 30 31 32 34 37 38 39 46 48 49 52 61 65 68 69 70
5 8 9 10 11 14 15 18 21 22 24 29 30 40 43 45 48 49 54 58 60 64 67 69 70
1 3 4 5 8 10 11 15 23 30 33 36 44 47 48 49 50 51 53 56 59 63 66 69 70
2 3 11 17 18 26 27 29 33 38 42 44 46 48 50 51 52 56 58 61 62 63 64 65 66
4 6 7 8 14 21 23 24 28 35 36 39 41 45 47 51 53 54 55 57 60 63 64 69 70
1 7 11 13 14 16 17 19 20 22 25 27 35 36 38 41 46 48 52 53 54 61 64 65 67
4 5 14 17 19 23 25 30 31 32 33 40 43 46 47 50 52 54 56 58 61 62 66 67 68
3 6 7 8 13 18 22 27 29 31 32 35 38 40 41 43 44 55 57 62 65 67 68 69 70
2 3 8 12 14 17 19 20 21 24 25 26 34 37 42 44 45 46 52 54 60 61 64 69 70
3 7 9 11 13 16 19 20 21 24 25 33 35 40 41 43 44 45 48 50 51 56 60 63 66
2 3 5 6 9 13 16 17 22 26 30 31 32 36 42 44 46 52 53 55 57 59 61 64 68
3 5 7 9 12 14 16 28 30 34 35 36 37 39 40 41 43 44 53 54 58 59 62 69 70
2 4 5 6 16 18 21 23 24 26 29 30 33 34 37 42 45 47 50 55 56 57 60 66 67
1 3 4 8 9 10 12 13 14 15 16 18 23 27 29 34 37 38 44 47 49 54 58 65 67
1 2 4 6 11 12 14 18 20 22 23 26 29 36 42 47 48 53 54 55 57 58 59 62 64
2 7 10 13 15 21 22 24 26 27 34 35 37 38 41 42 45 49 51 58 59 60 62 63 65
1 3 4 6 10 15 19 20 21 22 23 24 25 31 32 44 45 47 49 55 57 58 60 62 68
2 4 8 9 12 13 19 23 25 26 27 31 32 36 38 42 47 51 53 58 63 65 68 69 70
2 7 9 10 14 15 18 20 26 29 31 32 33 35 36 41 42 49 50 53 54 56 66 67 68
8 10 12 15 16 17 21 22 24 28 33 36 39 45 46 49 50 52 53 56 58 60 61 62 66
4 6 9 11 12 13 17 21 23 24 27 38 40 43 45 46 47 48 52 55 57 59 60 61 65
3 6 11 12 14 22 28 31 32 33 34 37 39 44 48 50 51 54 55 56 57 63 66 67 68
1 5 9 10 12 13 15 16 19 20 22 25 30 31 32 34 37 40 43 49 51 59 63 64 68

Citations

• https://ljcr.dmgordon.org/cover/show_cover.php?v=70&k=25&t=3 pending

Machine verification

• Certificate check passed score 37 2026-11-12 17:32 UTC
  Valid (70,25,3) covering with 37 blocks.

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