The results refer to the Hadamard matrices of order 24 found by
Ito, Leon, Longyear and Kimura from Neil Sloane's page.
A defining set is a set of elements of a design or Hadamard matrix
from which the remaining matrix may be reconstructed uniquely.
The first 10 11 row defining sets he found were
Subset 1 2 3 4 5 12 18 19 20 21 22
Subset 1 2 3 4 5 12 18 19 20 22 23
Subset 1 2 3 4 5 12 18 19 21 22 23
Subset 1 2 3 4 5 12 18 20 21 22 23
Subset 1 2 3 4 5 12 19 20 21 22 23
Subset 1 2 3 4 5 13 18 19 20 21 22
Subset 1 2 3 4 5 13 18 19 20 21 23
Subset 1 2 3 4 5 13 18 19 20 22 23
Subset 1 2 3 4 5 13 18 19 21 22 23
Subset 1 2 3 4 5 13 18 20 21 22 23
where the numbers are the row numbers of the original Hadamard design.
Jan 6, 2000 02:07:29
All 10-row subsets of [had.24.2.txt] were tested and no
10 row defining sets found.
All C(23,11) 11-row subsets were tested and
154188 / 1352078 11-row defining sets found.
The first 5 defining sets found were
Subset 1 2 3 4 5 12 13 14 15 18 21
Subset 1 2 3 4 5 12 13 14 15 18 23
Subset 1 2 3 4 5 12 13 14 15 19 21
Subset 1 2 3 4 5 12 13 14 15 19 23
Subset 1 2 3 4 5 12 13 14 16 18 21
Jan 19, 2000 01:27:09 pm +1100
All 10-row subsets of [had.24.3.txt] were tested and no
10 row defining sets found.
All C(23,11) 11-row subsets were tested and
107604 / 1352078 11-row defining sets found.
The first 5 11-row defining sets found were
Subset 1 2 3 4 5 12 13 17 18 19 22
Subset 1 2 3 4 5 12 13 17 18 20 21
Subset 1 2 3 4 5 12 13 17 18 21 22
Subset 1 2 3 4 5 12 13 17 19 20 21
Subset 1 2 3 4 5 12 13 17 19 21 22
From vdd02@uow.edu.au Wed Jan 26 16:48:50 2000 +1100
All 10-row subsets of [had.24.4.txt] were tested and no
10 row defining sets found.
All C(23,11) 11-row subsets were tested and
220742 / 1352078 11-row defining sets found.
The first 5 11-row defining sets found were
Subset 1 2 3 4 5 12 13 14 15 16 18
Subset 1 2 3 4 5 12 13 14 15 16 20
Subset 1 2 3 4 5 12 13 14 15 17 18
Subset 1 2 3 4 5 12 13 14 15 17 20
Subset 1 2 3 4 5 12 13 14 15 18 20