Bounds on the number of Hadamard designs of even order
Why this work is in the frame
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Bibliographic record
Abstract
Abstract A new lower bound on the number of non‐isomorphic Hadamard symmetric designs of even order is proved. The new bound improves the bound on the number of Hadamard designs of order 2 n given in [12] by a factor of 8 n − 1 for every odd n > 1, and for every even n such that 4 n − 1 > 7 is a prime. For orders 8, 10, and 12, the number of non‐isomorphic Hadamard designs is shown to be at least 22,478,260, 1.31 × 10 15 , and 10 27 , respectively. For orders 2 n = 14, 16, 18 and 20, a lower bound of (4 n − 1)! is proved. It is conjectured that (4 n − 1)! is a lower bound for all orders 2 n ≥ 14. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 363‐378, 2001
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it