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zeekay b832ba2c39 Initial Torus commit 
Forked from upstream concrete (BSD-3-Clause-Clear, © 2024 ZAMA) at HEAD
ecb729bb. Modifications copyright © 2026 Lux Industries Inc.

Rebranding scope:
  - Python module concrete → torus (across frontends/torus-python)
  - Rust module concrete-* → torus-* (across frontends/torus-rust)
  - MLIR dialect concretelang → toruslang (across compilers/torus-compiler)
  - Compiler optimizer concrete-optimizer → torus-optimizer
  - Backend concrete-cpu / concrete-cuda → torus-cpu / torus-cuda
  - Wire protocol concrete-protocol → torus-protocol
  - Parameter-curves concrete-security-curves-* → torus-security-curves-*
  - Public symbols concretelib → toruslib, ConcreteLang → TorusLang
  - URLs github.com/zama-ai/concrete → github.com/luxfhe/torus
  - URLs docs.zama.ai/concrete → docs.luxfhe.com/torus

Legal compliance:
  - LICENSE.txt retains original Copyright © 2024 ZAMA verbatim (§1-§2)
  - LICENSE.txt adds modifications copyright © 2026 Lux Industries Inc.
  - §3 endorsement clause: Torus is marketed exclusively as a Lux product;
    no Zama name used in README, docs, or marketing
  - NOTICE file provides factual attribution per legal best practice
    (not endorsement; required by upstream BSD-3-Clause-Clear)

README + NOTICE rewritten from scratch with Lux brand:
  - Quick-start in Python (torus.fhe)
  - Architecture diagram showing the gen-1 vtbl integration path
    (luxcpp/gpu → lux-private/gpu-kernels for CUDA/Metal/WebGPU)
  - Scheme coverage table: TFHE (luxfi/fhe), CKKS/BGV/BFV (luxfi/lattice)
  - Lux FHE family table: Torus / TorusVM / TorusEVM / TorusML / TorusNet

Known limitations (phase-2A scope):
  - PyPI package torus-fhe not yet published; the torus Python module
    is renamed structurally but pip-installable distribution is a
    follow-up (Phase 2A.1)
  - MLIR dialect rename is text-level; the compiler-internal LLVM
    rebuild (concrete-compiler-internal-llvm-project submodule) is
    structural and works; tablegen files renamed concrete→torus but the
    generated .inc files in the source tree will regenerate at build
    time
  - backends/torus-cuda/implementation/ is an upstream submodule
    pointer to the tfhe-rs source (not fetched in the staging clone);
    the CUDA backend body is delivered out-of-tree
  - ~100 test-fixture variable names like concrete_encoded_sample
    retain "concrete" as a math term (vs symbolic); these are inside
    tests/, not the public API; cleanup is a follow-up commit
  - 295 Python `from concrete import ...` residuals in luxfhe/ml-sdk
    consumer remain; that repo's import update is Phase 2B

This commit is the seed for the luxfhe/torus repo. Push as the first
commit to a fresh GitHub repo; do not re-import upstream Zama git
history.
2026-05-29 14:16:47 -07:00

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security level: 112
target p_error: 6.3e-5
per precision and log norm2:
- 1: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 4, 8, 512, 1, 13, 3, 3, 21, 2.4e-5
- 1 : 5, 8, 512, 1, 17, 3, 3, 26, 1.0e-5
- 2 : 5, 8, 512, 1, 17, 3, 3, 26, 1.3e-5
- 3 : 5, 8, 512, 1, 17, 3, 3, 26, 2.4e-5
- 4 : 5, 8, 520, 1, 17, 3, 3, 27, 6.1e-5
- 5 : 4, 8, 530, 2, 9, 4, 3, 32, 6.0e-5
- 6 : 6, 8, 512, 1, 21, 3, 3, 32, 6.1e-5
- 7 : 6, 8, 516, 1, 21, 3, 3, 32, 5.6e-5
- 8 : 6, 8, 544, 1, 21, 3, 3, 34, 6.0e-5
- 9 : 5, 8, 515, 2, 12, 3, 3, 38, 5.9e-5
- 10: 6, 8, 512, 2, 14, 3, 3, 46, 4.7e-5
- 11: 6, 8, 512, 2, 14, 3, 3, 46, 4.8e-5
- 12: 6, 8, 512, 2, 14, 3, 3, 46, 5.2e-5
- 13: 6, 8, 513, 2, 14, 3, 3, 46, 5.4e-5
- 14: 6, 8, 518, 2, 14, 3, 3, 46, 6.1e-5
- 15: 6, 8, 525, 2, 14, 5, 2, 50, 6.3e-5
- 16: 6, 8, 513, 3, 11, 3, 3, 60, 5.4e-5
- 17: 6, 8, 518, 3, 11, 3, 3, 61, 5.8e-5
- 18: 6, 8, 521, 3, 11, 5, 2, 64, 6.2e-5
- 19: 6, 8, 521, 4, 9, 3, 3, 75, 5.5e-5
- 20: 4, 9, 522, 3, 12, 3, 3, 84, 6.2e-5
- 21: 4, 9, 538, 3, 12, 3, 3, 86, 6.0e-5
- 22: 4, 9, 523, 4, 10, 3, 3, 103, 6.2e-5
- 23: 4, 9, 512, 4, 10, 5, 2, 105, 2.7e-5
- 24: 4, 9, 525, 5, 8, 3, 3, 123, 5.6e-5
- 25: 4, 9, 515, 5, 8, 5, 2, 124, 5.8e-5
- 26: 4, 9, 523, 6, 7, 5, 2, 145, 6.1e-5
- 27: 4, 9, 534, 7, 6, 6, 2, 170, 6.2e-5
- 28: 4, 9, 512, 11, 4, 5, 2, 236, 6.0e-6
- 29: 4, 9, 527, 14, 3, 6, 2, 303, 6.0e-5
- 30: 4, 9, 523, 22, 2, 6, 2, 454, 5.9e-5
# no solution starting from log norm2 = 31
- 2: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 5, 8, 610, 1, 17, 2, 5, 29, 5.8e-5
- 1 : 5, 8, 611, 1, 17, 2, 5, 29, 6.0e-5
- 2 : 5, 8, 579, 1, 17, 3, 4, 29, 6.1e-5
- 3 : 5, 8, 600, 1, 17, 3, 4, 30, 6.0e-5
- 4 : 6, 8, 580, 1, 21, 3, 4, 35, 6.0e-5
- 5 : 6, 8, 581, 1, 21, 3, 4, 35, 6.1e-5
- 6 : 6, 8, 586, 1, 21, 3, 4, 36, 5.9e-5
- 7 : 3, 9, 595, 1, 21, 3, 4, 39, 6.2e-5
- 8 : 5, 8, 562, 2, 12, 4, 3, 42, 5.8e-5
- 9 : 6, 8, 553, 2, 14, 4, 3, 51, 6.1e-5
- 10: 6, 8, 553, 2, 14, 4, 3, 51, 6.2e-5
- 11: 6, 8, 554, 2, 14, 4, 3, 51, 5.4e-5
- 12: 6, 8, 555, 2, 14, 4, 3, 51, 5.9e-5
- 13: 6, 8, 562, 2, 14, 4, 3, 51, 5.9e-5
- 14: 3, 9, 589, 2, 14, 7, 2, 61, 6.3e-5
- 15: 6, 8, 555, 3, 11, 4, 3, 66, 5.8e-5
- 16: 6, 8, 562, 3, 11, 4, 3, 67, 5.5e-5
- 17: 3, 9, 593, 3, 11, 7, 2, 78, 6.3e-5
- 18: 3, 9, 537, 4, 9, 5, 2, 83, 6.2e-5
- 19: 4, 9, 554, 3, 12, 4, 3, 91, 5.9e-5
- 20: 4, 9, 565, 3, 12, 4, 3, 92, 5.5e-5
- 21: 4, 9, 541, 4, 10, 5, 2, 111, 6.0e-5
- 22: 4, 9, 547, 4, 10, 6, 2, 114, 5.8e-5
- 23: 4, 9, 543, 5, 8, 5, 2, 131, 5.9e-5
- 24: 4, 9, 557, 5, 8, 6, 2, 136, 5.8e-5
- 25: 4, 9, 568, 6, 7, 6, 2, 160, 6.2e-5
- 26: 4, 9, 556, 8, 5, 6, 2, 197, 6.3e-5
- 27: 4, 9, 540, 11, 4, 6, 2, 251, 6.1e-5
- 28: 4, 9, 546, 15, 3, 6, 2, 334, 5.5e-5
- 29: 4, 9, 573, 22, 2, 6, 2, 497, 6.3e-5
# no solution starting from log norm2 = 30
- 3: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 2, 9, 579, 2, 9, 4, 3, 39, 6.0e-5
- 1 : 2, 9, 581, 2, 9, 4, 3, 39, 5.7e-5
- 2 : 2, 9, 590, 2, 9, 4, 3, 39, 5.6e-5
- 3 : 3, 9, 617, 1, 21, 3, 4, 40, 5.6e-5
- 4 : 3, 9, 618, 1, 21, 3, 4, 40, 6.0e-5
- 5 : 3, 9, 625, 1, 21, 3, 4, 40, 5.6e-5
- 6 : 4, 9, 626, 1, 23, 3, 4, 53, 6.1e-5
- 7 : 4, 9, 632, 1, 23, 3, 4, 53, 6.2e-5
- 8 : 3, 9, 590, 2, 14, 4, 3, 56, 5.4e-5
- 9 : 3, 9, 590, 2, 14, 4, 3, 56, 5.5e-5
- 10: 3, 9, 590, 2, 14, 4, 3, 56, 6.0e-5
- 11: 3, 9, 592, 2, 14, 4, 3, 56, 5.9e-5
- 12: 3, 9, 602, 2, 14, 4, 3, 57, 6.0e-5
- 13: 3, 9, 590, 3, 11, 4, 3, 72, 6.0e-5
- 14: 3, 9, 592, 3, 11, 4, 3, 73, 5.9e-5
- 15: 3, 9, 602, 3, 11, 4, 3, 74, 6.0e-5
- 16: 3, 9, 593, 4, 9, 4, 3, 89, 5.8e-5
- 17: 3, 9, 608, 4, 9, 4, 3, 91, 6.1e-5
- 18: 4, 9, 603, 3, 12, 4, 3, 98, 5.8e-5
- 19: 4, 9, 645, 3, 12, 4, 3, 104, 6.3e-5
- 20: 4, 9, 604, 4, 10, 4, 3, 120, 6.3e-5
- 21: 4, 9, 629, 4, 10, 7, 2, 132, 6.3e-5
- 22: 4, 9, 584, 5, 8, 6, 2, 142, 6.0e-5
- 23: 4, 9, 586, 6, 7, 6, 2, 164, 5.8e-5
- 24: 4, 9, 588, 7, 6, 6, 2, 186, 6.3e-5
- 25: 4, 9, 594, 9, 5, 6, 2, 232, 5.9e-5
- 26: 4, 9, 602, 11, 4, 6, 2, 279, 6.2e-5
- 27: 4, 9, 617, 15, 3, 7, 2, 378, 6.3e-5
- 28: 4, 9, 598, 44, 1, 13, 1, 1016, 6.1e-5
# no solution starting from log norm2 = 29
- 4: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 10, 624, 2, 9, 4, 3, 53, 5.8e-5
- 1 : 1, 10, 648, 2, 9, 4, 3, 55, 6.3e-5
- 2 : 2, 10, 678, 1, 23, 3, 4, 65, 6.0e-5
- 3 : 2, 10, 678, 1, 23, 3, 4, 65, 6.2e-5
- 4 : 2, 10, 679, 1, 23, 3, 4, 65, 6.2e-5
- 5 : 2, 10, 684, 1, 23, 3, 4, 66, 6.3e-5
- 6 : 2, 10, 701, 1, 23, 3, 5, 67, 6.2e-5
- 7 : 2, 10, 650, 2, 15, 4, 3, 92, 6.1e-5
- 8 : 2, 10, 650, 2, 15, 4, 3, 92, 6.1e-5
- 9 : 2, 10, 650, 2, 15, 4, 3, 92, 6.1e-5
- 10: 2, 10, 650, 2, 15, 4, 3, 92, 6.2e-5
- 11: 2, 10, 651, 2, 15, 4, 3, 92, 6.1e-5
- 12: 2, 10, 654, 2, 15, 4, 3, 92, 6.2e-5
- 13: 2, 10, 641, 2, 15, 5, 3, 93, 6.2e-5
- 14: 2, 10, 634, 3, 12, 5, 3, 118, 6.2e-5
- 15: 2, 10, 635, 3, 12, 5, 3, 119, 5.6e-5
- 16: 2, 10, 637, 3, 12, 5, 3, 119, 5.7e-5
- 17: 2, 10, 648, 3, 12, 5, 3, 121, 6.1e-5
- 18: 2, 10, 613, 4, 9, 7, 2, 145, 5.7e-5
- 19: 2, 10, 620, 4, 9, 7, 2, 146, 6.0e-5
- 20: 2, 10, 616, 5, 8, 7, 2, 171, 5.4e-5
- 21: 2, 10, 642, 5, 8, 7, 2, 177, 6.2e-5
- 22: 2, 10, 663, 6, 7, 8, 2, 213, 6.3e-5
- 23: 2, 10, 626, 8, 5, 7, 2, 250, 5.9e-5
- 24: 2, 10, 622, 11, 4, 7, 2, 325, 6.3e-5
- 25: 2, 10, 639, 14, 3, 7, 2, 413, 6.1e-5
- 26: 2, 10, 656, 22, 2, 8, 2, 641, 6.3e-5
# no solution starting from log norm2 = 27
- 5: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 11, 669, 1, 23, 5, 3, 89, 6.2e-5
- 1 : 1, 11, 669, 1, 23, 5, 3, 89, 6.2e-5
- 2 : 1, 11, 670, 1, 23, 5, 3, 89, 5.4e-5
- 3 : 1, 11, 670, 1, 23, 5, 3, 89, 6.1e-5
- 4 : 1, 11, 673, 1, 23, 5, 3, 89, 6.3e-5
- 5 : 1, 11, 695, 1, 23, 5, 3, 92, 6.3e-5
- 6 : 1, 11, 669, 2, 15, 5, 3, 125, 6.2e-5
- 7 : 1, 11, 669, 2, 15, 5, 3, 125, 6.2e-5
- 8 : 1, 11, 669, 2, 15, 5, 3, 125, 6.2e-5
- 9 : 1, 11, 669, 2, 15, 5, 3, 125, 6.3e-5
- 10: 1, 11, 670, 2, 15, 5, 3, 125, 5.8e-5
- 11: 1, 11, 672, 2, 15, 5, 3, 126, 5.8e-5
- 12: 1, 11, 683, 2, 15, 5, 3, 128, 5.9e-5
- 13: 1, 11, 670, 3, 11, 5, 3, 162, 5.6e-5
- 14: 1, 11, 671, 3, 11, 5, 3, 162, 5.9e-5
- 15: 1, 11, 678, 3, 11, 5, 3, 164, 5.7e-5
- 16: 1, 11, 649, 4, 9, 7, 2, 198, 6.2e-5
- 17: 1, 11, 653, 4, 9, 7, 2, 199, 5.8e-5
- 18: 1, 11, 695, 4, 9, 5, 3, 206, 6.3e-5
- 19: 1, 11, 670, 5, 8, 7, 2, 240, 6.0e-5
- 20: 1, 11, 670, 6, 7, 8, 2, 280, 6.2e-5
- 21: 1, 11, 678, 7, 6, 8, 2, 320, 6.3e-5
- 22: 1, 11, 666, 10, 4, 7, 2, 421, 6.1e-5
- 23: 1, 11, 663, 14, 3, 7, 2, 564, 6.2e-5
- 24: 1, 11, 681, 21, 2, 8, 2, 843, 6.1e-5
# no solution starting from log norm2 = 25
- 6: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 12, 751, 1, 22, 4, 4, 203, 5.7e-5
- 1 : 1, 12, 752, 1, 22, 4, 4, 204, 5.6e-5
- 2 : 1, 12, 755, 1, 22, 4, 4, 204, 6.0e-5
- 3 : 1, 12, 781, 1, 22, 4, 4, 211, 6.3e-5
- 4 : 1, 12, 730, 2, 15, 5, 3, 289, 5.7e-5
- 5 : 1, 12, 730, 2, 15, 5, 3, 289, 5.7e-5
- 6 : 1, 12, 730, 2, 15, 5, 3, 289, 5.7e-5
- 7 : 1, 12, 730, 2, 15, 5, 3, 289, 5.8e-5
- 8 : 1, 12, 730, 2, 15, 5, 3, 289, 6.3e-5
- 9 : 1, 12, 733, 2, 15, 5, 3, 290, 6.0e-5
- 10: 1, 12, 764, 2, 15, 4, 4, 296, 5.9e-5
- 11: 1, 12, 730, 3, 11, 5, 3, 375, 6.0e-5
- 12: 1, 12, 732, 3, 11, 5, 3, 376, 5.7e-5
- 13: 1, 12, 739, 3, 11, 5, 3, 379, 5.9e-5
- 14: 1, 12, 748, 3, 11, 9, 2, 407, 6.2e-5
- 15: 1, 12, 705, 4, 9, 8, 2, 462, 6.2e-5
- 16: 1, 12, 725, 4, 9, 8, 2, 474, 6.1e-5
- 17: 1, 12, 725, 5, 8, 8, 2, 559, 6.2e-5
- 18: 1, 12, 737, 6, 7, 8, 2, 655, 6.2e-5
- 19: 1, 12, 749, 7, 6, 9, 2, 759, 6.3e-5
- 20: 1, 12, 715, 10, 4, 8, 2, 971, 6.0e-5
- 21: 1, 12, 716, 14, 3, 8, 2, 1308, 6.2e-5
- 22: 1, 12, 735, 21, 2, 9, 2, 1951, 6.1e-5
# no solution starting from log norm2 = 23
- 7: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 13, 780, 1, 22, 6, 3, 470, 6.0e-5
- 1 : 1, 13, 791, 1, 22, 6, 3, 477, 6.1e-5
- 2 : 1, 13, 777, 2, 15, 6, 3, 663, 6.3e-5
- 3 : 1, 13, 778, 2, 15, 6, 3, 664, 5.4e-5
- 4 : 1, 13, 778, 2, 15, 6, 3, 664, 5.4e-5
- 5 : 1, 13, 778, 2, 15, 6, 3, 664, 5.5e-5
- 6 : 1, 13, 778, 2, 15, 6, 3, 664, 5.9e-5
- 7 : 1, 13, 780, 2, 15, 6, 3, 665, 5.6e-5
- 8 : 1, 13, 788, 2, 15, 6, 3, 672, 6.1e-5
- 9 : 1, 13, 778, 3, 11, 6, 3, 858, 5.6e-5
- 10: 1, 13, 779, 3, 11, 6, 3, 859, 5.5e-5
- 11: 1, 13, 782, 3, 11, 6, 3, 863, 6.1e-5
- 12: 1, 13, 811, 3, 11, 6, 3, 893, 6.2e-5
- 13: 1, 13, 782, 4, 9, 6, 3, 1058, 5.7e-5
- 14: 1, 13, 804, 4, 9, 6, 3, 1087, 6.1e-5
- 15: 1, 13, 784, 5, 8, 9, 2, 1293, 6.2e-5
- 16: 1, 13, 800, 6, 7, 10, 2, 1532, 6.3e-5
- 17: 1, 13, 763, 8, 5, 9, 2, 1832, 6.1e-5
- 18: 1, 13, 768, 10, 4, 9, 2, 2228, 5.9e-5
- 19: 1, 13, 772, 14, 3, 9, 2, 3011, 5.9e-5
- 20: 1, 13, 794, 21, 2, 10, 2, 4498, 6.3e-5
# no solution starting from log norm2 = 21
- 8: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 14, 840, 2, 15, 6, 3, 1508, 5.9e-5
- 1 : 1, 14, 840, 2, 15, 6, 3, 1508, 6.0e-5
- 2 : 1, 14, 840, 2, 15, 6, 3, 1508, 6.0e-5
- 3 : 1, 14, 840, 2, 15, 6, 3, 1508, 6.1e-5
- 4 : 1, 14, 841, 2, 15, 6, 3, 1509, 5.9e-5
- 5 : 1, 14, 844, 2, 15, 6, 3, 1514, 5.9e-5
- 6 : 1, 14, 870, 2, 15, 5, 4, 1532, 6.3e-5
- 7 : 1, 14, 840, 3, 11, 6, 3, 1954, 6.2e-5
- 8 : 1, 14, 841, 3, 11, 6, 3, 1956, 6.3e-5
- 9 : 1, 14, 847, 3, 11, 6, 3, 1970, 6.1e-5
- 10: 1, 14, 858, 3, 11, 7, 3, 2021, 6.2e-5
- 11: 1, 14, 837, 4, 9, 7, 3, 2418, 5.7e-5
- 12: 1, 14, 861, 4, 9, 7, 3, 2485, 6.3e-5
- 13: 1, 14, 849, 5, 8, 10, 2, 2982, 6.3e-5
- 14: 1, 14, 868, 6, 6, 11, 2, 3536, 6.3e-5
- 15: 1, 14, 818, 8, 5, 10, 2, 4180, 6.1e-5
- 16: 1, 14, 822, 10, 4, 10, 2, 5073, 6.2e-5
- 17: 1, 14, 828, 14, 3, 10, 2, 6869, 6.3e-5
- 18: 1, 14, 870, 21, 2, 11, 2, 10477, 6.3e-5
# no solution starting from log norm2 = 19
- 9: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 15, 916, 2, 15, 5, 4, 3391, 5.9e-5
- 1 : 1, 15, 916, 2, 15, 5, 4, 3391, 6.0e-5
- 2 : 1, 15, 917, 2, 15, 5, 4, 3395, 5.8e-5
- 3 : 1, 15, 919, 2, 15, 5, 4, 3402, 6.2e-5
- 4 : 1, 15, 898, 2, 15, 7, 3, 3440, 6.2e-5
- 5 : 1, 15, 886, 3, 11, 7, 3, 4392, 5.7e-5
- 6 : 1, 15, 887, 3, 11, 7, 3, 4397, 5.6e-5
- 7 : 1, 15, 890, 3, 11, 7, 3, 4411, 5.9e-5
- 8 : 1, 15, 914, 3, 11, 7, 3, 4527, 6.3e-5
- 9 : 1, 15, 891, 4, 9, 7, 3, 5418, 5.9e-5
- 10: 1, 15, 933, 4, 9, 7, 3, 5668, 6.3e-5
- 11: 1, 15, 910, 5, 7, 7, 3, 6555, 6.3e-5
- 12: 1, 15, 914, 6, 6, 7, 3, 7612, 6.3e-5
- 13: 1, 15, 874, 8, 5, 11, 2, 9469, 5.9e-5
- 14: 1, 15, 878, 10, 4, 11, 2, 11488, 6.2e-5
- 15: 1, 15, 887, 14, 3, 11, 2, 15596, 6.3e-5
- 16: 1, 15, 882, 41, 1, 11, 2, 42299, 6.2e-5
# no solution starting from log norm2 = 17
- 10: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 16, 952, 2, 14, 7, 3, 7635, 6.1e-5
- 1 : 1, 16, 969, 2, 14, 6, 4, 7645, 6.1e-5
- 2 : 1, 16, 977, 2, 14, 6, 4, 7706, 6.2e-5
- 3 : 1, 16, 951, 3, 11, 7, 3, 9886, 6.3e-5
- 4 : 1, 16, 941, 3, 11, 8, 3, 9902, 6.0e-5
- 5 : 1, 16, 945, 3, 11, 8, 3, 9943, 5.7e-5
- 6 : 1, 16, 971, 3, 11, 8, 3, 10210, 6.2e-5
- 7 : 1, 16, 946, 4, 9, 8, 3, 12200, 5.9e-5
- 8 : 1, 16, 973, 4, 9, 12, 2, 13028, 6.3e-5
- 9 : 1, 16, 956, 5, 7, 8, 3, 14597, 6.1e-5
- 10: 1, 16, 938, 6, 6, 11, 2, 16907, 6.3e-5
- 11: 1, 16, 933, 8, 5, 11, 2, 21250, 6.0e-5
- 12: 1, 16, 939, 10, 4, 11, 2, 25845, 6.2e-5
- 13: 1, 16, 950, 14, 3, 12, 2, 35289, 6.2e-5
- 14: 1, 16, 949, 40, 1, 12, 2, 93853, 6.3e-5
# no solution starting from log norm2 = 15
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