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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: 96
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, 16, 2, 5, 20, 1.2e-17
- 1 : 4, 8, 512, 1, 16, 2, 5, 20, 2.2e-16
- 2 : 4, 8, 512, 1, 16, 2, 5, 20, 7.0e-13
- 3 : 4, 8, 512, 1, 16, 2, 5, 20, 2.6e-7
- 4 : 5, 8, 512, 1, 20, 2, 5, 25, 1.2e-15
- 5 : 5, 8, 512, 1, 20, 2, 5, 25, 7.1e-15
- 6 : 5, 8, 512, 1, 20, 2, 5, 25, 1.7e-12
- 7 : 5, 8, 512, 1, 20, 2, 5, 25, 6.8e-8
- 8 : 4, 8, 512, 2, 11, 2, 5, 29, 1.8e-6
- 9 : 6, 8, 512, 1, 24, 2, 5, 30, 3.9e-12
- 10: 6, 8, 512, 1, 24, 2, 5, 30, 1.4e-8
- 11: 6, 8, 512, 1, 24, 4, 3, 33, 5.4e-5
- 12: 5, 8, 512, 2, 14, 2, 5, 36, 2.0e-13
- 13: 5, 8, 512, 2, 14, 2, 5, 36, 2.5e-9
- 14: 5, 8, 512, 2, 14, 3, 4, 38, 3.9e-5
- 15: 6, 8, 512, 2, 16, 2, 5, 44, 5.7e-14
- 16: 6, 8, 512, 2, 16, 2, 5, 44, 3.0e-13
- 17: 6, 8, 512, 2, 16, 2, 5, 44, 5.2e-11
- 18: 6, 8, 512, 2, 16, 2, 5, 44, 7.4e-7
- 19: 6, 8, 512, 3, 12, 2, 5, 58, 7.2e-14
- 20: 6, 8, 512, 3, 12, 2, 5, 58, 7.1e-13
- 21: 6, 8, 512, 3, 12, 2, 5, 58, 4.3e-10
- 22: 6, 8, 512, 3, 12, 2, 5, 58, 8.8e-6
- 23: 6, 8, 512, 4, 10, 2, 5, 72, 1.3e-9
- 24: 6, 8, 512, 4, 10, 2, 5, 72, 2.7e-5
- 25: 6, 8, 512, 5, 8, 2, 5, 86, 1.1e-8
- 26: 6, 8, 512, 5, 8, 3, 4, 88, 5.5e-5
- 27: 6, 8, 512, 7, 6, 2, 5, 114, 1.1e-7
- 28: 6, 8, 512, 9, 5, 2, 5, 142, 4.7e-7
- 29: 6, 8, 512, 11, 4, 2, 5, 170, 2.6e-6
- 30: 6, 8, 512, 15, 3, 2, 5, 226, 2.0e-5
- 31: 6, 8, 512, 44, 1, 2, 5, 632, 5.0e-5
- 2: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 4, 8, 512, 1, 16, 2, 5, 20, 1.9e-5
- 1 : 4, 8, 512, 1, 16, 2, 5, 20, 4.0e-5
- 2 : 4, 8, 512, 1, 16, 3, 4, 21, 1.7e-5
- 3 : 5, 8, 512, 1, 20, 2, 5, 25, 5.6e-5
- 4 : 5, 8, 512, 1, 20, 2, 5, 25, 6.3e-5
- 5 : 5, 8, 516, 1, 20, 2, 5, 25, 5.5e-5
- 6 : 5, 8, 540, 1, 20, 2, 5, 26, 6.3e-5
- 7 : 4, 8, 512, 2, 11, 3, 4, 30, 4.7e-5
- 8 : 6, 8, 521, 1, 24, 2, 5, 31, 5.8e-5
- 9 : 6, 8, 536, 1, 24, 2, 5, 32, 6.2e-5
- 10: 5, 8, 512, 2, 14, 2, 5, 36, 6.0e-5
- 11: 5, 8, 514, 2, 14, 2, 5, 36, 6.0e-5
- 12: 5, 8, 525, 2, 14, 2, 5, 37, 6.2e-5
- 13: 6, 8, 518, 2, 16, 2, 5, 45, 5.6e-5
- 14: 6, 8, 518, 2, 16, 2, 5, 45, 5.8e-5
- 15: 6, 8, 519, 2, 16, 2, 5, 45, 5.8e-5
- 16: 6, 8, 523, 2, 16, 2, 5, 45, 6.3e-5
- 17: 6, 8, 512, 2, 16, 3, 4, 46, 3.2e-5
- 18: 6, 8, 518, 3, 12, 2, 5, 59, 5.9e-5
- 19: 6, 8, 519, 3, 12, 2, 5, 59, 6.3e-5
- 20: 6, 8, 512, 3, 12, 3, 4, 60, 1.3e-6
- 21: 6, 8, 512, 3, 12, 4, 3, 61, 4.1e-5
- 22: 6, 8, 512, 4, 10, 3, 4, 74, 1.9e-6
- 23: 6, 8, 512, 4, 10, 7, 2, 80, 6.2e-5
- 24: 6, 8, 512, 5, 8, 3, 4, 88, 4.4e-6
- 25: 6, 8, 512, 6, 7, 3, 4, 102, 6.5e-6
- 26: 6, 8, 512, 7, 6, 3, 4, 116, 1.2e-5
- 27: 6, 8, 512, 9, 5, 3, 4, 144, 2.5e-5
- 28: 6, 8, 512, 11, 4, 3, 4, 172, 6.1e-5
- 29: 6, 8, 512, 15, 3, 6, 2, 232, 5.4e-5
- 30: 6, 8, 512, 45, 1, 4, 3, 649, 3.5e-5
# no solution starting from log norm2 = 31
- 3: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 2, 9, 513, 1, 16, 3, 4, 24, 5.8e-5
- 1 : 2, 9, 512, 1, 16, 4, 3, 25, 5.9e-5
- 2 : 2, 9, 512, 2, 11, 3, 4, 34, 2.7e-5
- 3 : 2, 9, 512, 2, 11, 3, 4, 34, 2.8e-5
- 4 : 2, 9, 512, 2, 11, 3, 4, 34, 3.7e-5
- 5 : 2, 9, 515, 2, 11, 3, 4, 34, 5.4e-5
- 6 : 3, 9, 519, 1, 23, 3, 4, 34, 5.9e-5
- 7 : 3, 9, 522, 1, 23, 3, 4, 35, 5.5e-5
- 8 : 3, 9, 538, 1, 23, 3, 4, 35, 6.3e-5
- 9 : 3, 9, 518, 2, 16, 3, 4, 49, 6.2e-5
- 10: 3, 9, 518, 2, 16, 3, 4, 49, 6.2e-5
- 11: 3, 9, 518, 2, 16, 3, 4, 49, 6.2e-5
- 12: 3, 9, 519, 2, 16, 3, 4, 49, 5.0e-5
- 13: 3, 9, 519, 2, 16, 3, 4, 49, 5.4e-5
- 14: 3, 9, 520, 2, 16, 3, 4, 49, 5.9e-5
- 15: 3, 9, 527, 2, 16, 3, 4, 49, 5.8e-5
- 16: 3, 9, 519, 3, 12, 3, 4, 63, 5.1e-5
- 17: 3, 9, 519, 3, 12, 3, 4, 63, 5.7e-5
- 18: 3, 9, 521, 3, 12, 3, 4, 63, 5.8e-5
- 19: 3, 9, 512, 3, 12, 4, 3, 64, 3.8e-5
- 20: 3, 9, 522, 4, 9, 3, 4, 77, 5.5e-5
- 21: 3, 9, 513, 4, 9, 4, 3, 78, 6.0e-5
- 22: 3, 9, 512, 5, 8, 4, 3, 92, 5.9e-6
- 23: 3, 9, 528, 5, 8, 4, 3, 94, 6.2e-5
- 24: 3, 9, 512, 6, 7, 7, 2, 110, 5.9e-5
- 25: 3, 9, 523, 8, 5, 4, 3, 136, 6.2e-5
- 26: 3, 9, 512, 11, 4, 4, 3, 176, 2.7e-5
- 27: 3, 9, 518, 14, 3, 7, 2, 225, 6.3e-5
- 28: 3, 9, 515, 22, 2, 7, 2, 336, 6.2e-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, 544, 1, 16, 7, 2, 36, 6.3e-5
- 1 : 1, 10, 521, 2, 11, 4, 3, 45, 5.4e-5
- 2 : 1, 10, 521, 2, 11, 4, 3, 45, 5.8e-5
- 3 : 1, 10, 523, 2, 11, 4, 3, 45, 5.6e-5
- 4 : 1, 10, 532, 2, 11, 4, 3, 46, 5.8e-5
- 5 : 2, 10, 572, 1, 23, 3, 4, 56, 6.0e-5
- 6 : 2, 10, 562, 1, 23, 4, 3, 57, 6.1e-5
- 7 : 1, 10, 512, 3, 8, 7, 2, 61, 6.3e-5
- 8 : 1, 10, 517, 4, 6, 6, 2, 73, 6.1e-5
- 9 : 2, 10, 545, 2, 15, 4, 3, 78, 5.9e-5
- 10: 2, 10, 545, 2, 15, 4, 3, 78, 6.0e-5
- 11: 2, 10, 545, 2, 15, 4, 3, 78, 6.3e-5
- 12: 2, 10, 547, 2, 15, 4, 3, 79, 6.1e-5
- 13: 2, 10, 539, 2, 15, 5, 3, 80, 5.3e-5
- 14: 2, 10, 572, 2, 15, 5, 3, 84, 6.2e-5
- 15: 2, 10, 546, 3, 12, 4, 3, 101, 5.9e-5
- 16: 2, 10, 536, 3, 12, 5, 3, 101, 5.5e-5
- 17: 2, 10, 542, 3, 12, 5, 3, 102, 6.3e-5
- 18: 2, 10, 515, 4, 9, 7, 2, 123, 5.9e-5
- 19: 2, 10, 520, 4, 9, 7, 2, 124, 5.3e-5
- 20: 2, 10, 517, 5, 8, 7, 2, 144, 5.4e-5
- 21: 2, 10, 530, 5, 8, 7, 2, 148, 5.9e-5
- 22: 2, 10, 535, 6, 7, 7, 2, 171, 6.2e-5
- 23: 2, 10, 545, 7, 6, 7, 2, 196, 6.1e-5
- 24: 2, 10, 558, 10, 4, 7, 2, 270, 6.2e-5
- 25: 2, 10, 529, 14, 3, 7, 2, 343, 5.7e-5
- 26: 2, 10, 534, 22, 2, 7, 2, 521, 6.1e-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, 565, 1, 23, 5, 3, 76, 5.2e-5
- 1 : 1, 11, 565, 1, 23, 5, 3, 76, 5.2e-5
- 2 : 1, 11, 565, 1, 23, 5, 3, 76, 5.3e-5
- 3 : 1, 11, 565, 1, 23, 5, 3, 76, 6.0e-5
- 4 : 1, 11, 567, 1, 23, 5, 3, 76, 6.0e-5
- 5 : 1, 11, 578, 1, 23, 5, 3, 78, 6.3e-5
- 6 : 1, 11, 565, 2, 15, 5, 3, 107, 5.1e-5
- 7 : 1, 11, 565, 2, 15, 5, 3, 107, 5.2e-5
- 8 : 1, 11, 565, 2, 15, 5, 3, 107, 5.2e-5
- 9 : 1, 11, 565, 2, 15, 5, 3, 107, 5.3e-5
- 10: 1, 11, 565, 2, 15, 5, 3, 107, 5.7e-5
- 11: 1, 11, 566, 2, 15, 5, 3, 107, 6.1e-5
- 12: 1, 11, 573, 2, 15, 5, 3, 108, 5.5e-5
- 13: 1, 11, 546, 3, 11, 7, 2, 138, 6.2e-5
- 14: 1, 11, 547, 3, 11, 7, 2, 138, 6.1e-5
- 15: 1, 11, 570, 3, 11, 5, 3, 139, 5.5e-5
- 16: 1, 11, 590, 3, 11, 8, 2, 150, 6.2e-5
- 17: 1, 11, 549, 4, 9, 7, 2, 168, 5.6e-5
- 18: 1, 11, 561, 4, 9, 7, 2, 172, 6.1e-5
- 19: 1, 11, 558, 5, 8, 7, 2, 202, 5.8e-5
- 20: 1, 11, 561, 6, 7, 7, 2, 233, 6.1e-5
- 21: 1, 11, 566, 7, 6, 7, 2, 266, 5.9e-5
- 22: 1, 11, 577, 8, 5, 8, 2, 305, 6.3e-5
- 23: 1, 11, 591, 11, 4, 8, 2, 409, 6.3e-5
- 24: 1, 11, 563, 21, 2, 8, 2, 698, 5.7e-5
- 25: 1, 11, 588, 44, 1, 16, 1, 1487, 6.3e-5
# no solution starting from log norm2 = 26
- 6: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 12, 635, 1, 22, 4, 4, 174, 6.0e-5
- 1 : 1, 12, 636, 1, 22, 4, 4, 175, 5.4e-5
- 2 : 1, 12, 638, 1, 22, 4, 4, 175, 5.6e-5
- 3 : 1, 12, 650, 1, 22, 4, 4, 178, 6.0e-5
- 4 : 1, 12, 616, 2, 15, 5, 3, 247, 5.7e-5
- 5 : 1, 12, 616, 2, 15, 5, 3, 247, 5.7e-5
- 6 : 1, 12, 616, 2, 15, 5, 3, 247, 5.8e-5
- 7 : 1, 12, 616, 2, 15, 5, 3, 247, 5.8e-5
- 8 : 1, 12, 616, 2, 15, 5, 3, 247, 6.2e-5
- 9 : 1, 12, 618, 2, 15, 5, 3, 247, 5.8e-5
- 10: 1, 12, 626, 2, 15, 5, 3, 250, 5.8e-5
- 11: 1, 12, 616, 3, 11, 5, 3, 319, 6.0e-5
- 12: 1, 12, 617, 3, 11, 5, 3, 319, 5.9e-5
- 13: 1, 12, 621, 3, 11, 5, 3, 321, 5.9e-5
- 14: 1, 12, 614, 3, 11, 8, 2, 332, 6.0e-5
- 15: 1, 12, 595, 4, 9, 8, 2, 392, 5.6e-5
- 16: 1, 12, 605, 4, 9, 8, 2, 398, 5.9e-5
- 17: 1, 12, 605, 5, 8, 8, 2, 469, 6.0e-5
- 18: 1, 12, 609, 6, 7, 8, 2, 544, 6.0e-5
- 19: 1, 12, 614, 7, 6, 8, 2, 620, 6.1e-5
- 20: 1, 12, 627, 8, 5, 9, 2, 711, 6.1e-5
- 21: 1, 12, 601, 14, 3, 8, 2, 1100, 5.9e-5
- 22: 1, 12, 610, 21, 2, 8, 2, 1617, 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, 660, 1, 22, 6, 3, 403, 6.0e-5
- 1 : 1, 13, 666, 1, 22, 6, 3, 406, 6.1e-5
- 2 : 1, 13, 659, 2, 15, 6, 3, 567, 5.2e-5
- 3 : 1, 13, 659, 2, 15, 6, 3, 567, 5.2e-5
- 4 : 1, 13, 659, 2, 15, 6, 3, 567, 5.2e-5
- 5 : 1, 13, 659, 2, 15, 6, 3, 567, 5.3e-5
- 6 : 1, 13, 659, 2, 15, 6, 3, 567, 5.6e-5
- 7 : 1, 13, 660, 2, 15, 6, 3, 568, 5.7e-5
- 8 : 1, 13, 665, 2, 15, 6, 3, 572, 5.6e-5
- 9 : 1, 13, 659, 3, 11, 6, 3, 732, 5.4e-5
- 10: 1, 13, 659, 3, 11, 6, 3, 732, 6.0e-5
- 11: 1, 13, 661, 3, 11, 6, 3, 734, 6.2e-5
- 12: 1, 13, 674, 3, 11, 6, 3, 748, 6.0e-5
- 13: 1, 13, 661, 4, 9, 6, 3, 899, 5.9e-5
- 14: 1, 13, 672, 4, 9, 6, 3, 914, 5.9e-5
- 15: 1, 13, 654, 5, 8, 9, 2, 1084, 5.7e-5
- 16: 1, 13, 658, 6, 7, 9, 2, 1255, 6.3e-5
- 17: 1, 13, 665, 7, 6, 9, 2, 1434, 6.2e-5
- 18: 1, 13, 683, 8, 5, 10, 2, 1654, 6.3e-5
- 19: 1, 13, 648, 14, 3, 9, 2, 2533, 6.2e-5
- 20: 1, 13, 657, 21, 2, 9, 2, 3717, 6.1e-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, 733, 1, 22, 21, 1, 1279, 6.3e-5
- 1 : 1, 14, 711, 2, 15, 6, 3, 1286, 5.8e-5
- 2 : 1, 14, 711, 2, 15, 6, 3, 1286, 5.8e-5
- 3 : 1, 14, 711, 2, 15, 6, 3, 1286, 5.9e-5
- 4 : 1, 14, 711, 2, 15, 6, 3, 1286, 6.2e-5
- 5 : 1, 14, 713, 2, 15, 6, 3, 1289, 5.9e-5
- 6 : 1, 14, 721, 2, 15, 6, 3, 1303, 6.0e-5
- 7 : 1, 14, 711, 3, 11, 6, 3, 1664, 6.0e-5
- 8 : 1, 14, 712, 3, 11, 6, 3, 1666, 5.7e-5
- 9 : 1, 14, 715, 3, 11, 6, 3, 1673, 5.8e-5
- 10: 1, 14, 719, 3, 11, 7, 3, 1704, 6.0e-5
- 11: 1, 14, 715, 4, 9, 6, 3, 2052, 5.9e-5
- 12: 1, 14, 720, 4, 9, 7, 3, 2089, 6.1e-5
- 13: 1, 14, 703, 5, 8, 10, 2, 2481, 6.1e-5
- 14: 1, 14, 706, 6, 6, 10, 2, 2866, 6.0e-5
- 15: 1, 14, 720, 7, 6, 10, 2, 3304, 6.3e-5
- 16: 1, 14, 694, 10, 4, 10, 2, 4293, 5.5e-5
- 17: 1, 14, 724, 13, 3, 10, 2, 5630, 6.3e-5
- 18: 1, 14, 706, 21, 2, 10, 2, 8492, 6.1e-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, 778, 2, 15, 5, 4, 2900, 5.5e-5
- 1 : 1, 15, 778, 2, 15, 5, 4, 2900, 5.6e-5
- 2 : 1, 15, 778, 2, 15, 5, 4, 2900, 5.9e-5
- 3 : 1, 15, 779, 2, 15, 5, 4, 2903, 6.3e-5
- 4 : 1, 15, 759, 2, 15, 7, 3, 2927, 6.0e-5
- 5 : 1, 15, 752, 3, 11, 7, 3, 3747, 6.1e-5
- 6 : 1, 15, 753, 3, 11, 7, 3, 3752, 5.5e-5
- 7 : 1, 15, 755, 3, 11, 7, 3, 3762, 5.6e-5
- 8 : 1, 15, 765, 3, 11, 7, 3, 3810, 6.3e-5
- 9 : 1, 15, 755, 4, 9, 7, 3, 4611, 6.0e-5
- 10: 1, 15, 769, 4, 9, 7, 3, 4694, 6.2e-5
- 11: 1, 15, 764, 5, 7, 7, 3, 5524, 6.0e-5
- 12: 1, 15, 765, 6, 6, 7, 3, 6392, 6.2e-5
- 13: 1, 15, 742, 8, 5, 10, 2, 8012, 5.9e-5
- 14: 1, 15, 741, 10, 4, 11, 2, 9715, 6.1e-5
- 15: 1, 15, 756, 13, 3, 11, 2, 12461, 6.0e-5
- 16: 1, 15, 757, 21, 2, 11, 2, 19290, 6.1e-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, 806, 2, 14, 7, 3, 6503, 6.2e-5
- 1 : 1, 16, 808, 2, 14, 7, 3, 6519, 5.8e-5
- 2 : 1, 16, 828, 2, 14, 6, 4, 6570, 6.2e-5
- 3 : 1, 16, 826, 2, 14, 12, 2, 7175, 6.3e-5
- 4 : 1, 16, 807, 3, 11, 7, 3, 8428, 5.9e-5
- 5 : 1, 16, 810, 3, 11, 7, 3, 8458, 6.1e-5
- 6 : 1, 16, 813, 3, 11, 8, 3, 8590, 6.0e-5
- 7 : 1, 16, 811, 4, 9, 7, 3, 10394, 6.3e-5
- 8 : 1, 16, 819, 4, 9, 8, 3, 10597, 6.0e-5
- 9 : 1, 16, 808, 5, 7, 8, 3, 12377, 5.7e-5
- 10: 1, 16, 790, 6, 6, 11, 2, 14280, 5.9e-5
- 11: 1, 16, 787, 8, 5, 11, 2, 17965, 6.3e-5
- 12: 1, 16, 790, 10, 4, 11, 2, 21785, 6.1e-5
- 13: 1, 16, 799, 13, 3, 12, 2, 27823, 6.1e-5
- 14: 1, 16, 827, 20, 2, 12, 2, 42538, 6.3e-5
# no solution starting from log norm2 = 15
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