MinT - Information on Result #1234029

Information on Result #1234029

Digital (80, 96, 1049631)-net over F₃₂, using (u,Â u+v)-construction based on

digital (12, 20, 1056)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (0, 0, 33)-net over F₃₂, using
    - s-reduction based on digital (0, 0, s)-net over F₃₂ for arbitrarily large s, using
      - arbitrary set of 32⁰ points [i]
  2. digital (0, 0, 33)-net over F₃₂ (see above)
  3. digital (0, 0, 33)-net over F₃₂ (see above)
  4. digital (0, 0, 33)-net over F₃₂ (see above)
  5. digital (0, 0, 33)-net over F₃₂ (see above)
  6. digital (0, 0, 33)-net over F₃₂ (see above)
  7. digital (0, 0, 33)-net over F₃₂ (see above)
  8. digital (0, 0, 33)-net over F₃₂ (see above)
  9. digital (0, 0, 33)-net over F₃₂ (see above)
  10. digital (0, 0, 33)-net over F₃₂ (see above)
  11. digital (0, 0, 33)-net over F₃₂ (see above)
  12. digital (0, 0, 33)-net over F₃₂ (see above)
  13. digital (0, 0, 33)-net over F₃₂ (see above)
  14. digital (0, 0, 33)-net over F₃₂ (see above)
  15. digital (0, 0, 33)-net over F₃₂ (see above)
  16. digital (0, 0, 33)-net over F₃₂ (see above)
  17. digital (0, 0, 33)-net over F₃₂ (see above)
  18. digital (0, 0, 33)-net over F₃₂ (see above)
  19. digital (0, 0, 33)-net over F₃₂ (see above)
  20. digital (0, 0, 33)-net over F₃₂ (see above)
  21. digital (0, 0, 33)-net over F₃₂ (see above)
  22. digital (0, 0, 33)-net over F₃₂ (see above)
  23. digital (0, 0, 33)-net over F₃₂ (see above)
  24. digital (0, 0, 33)-net over F₃₂ (see above)
  25. digital (0, 1, 33)-net over F₃₂, using
    - s-reduction based on digital (0, 1, s)-net over F₃₂ for arbitrarily large s, using
      - construction for strength kÂ =Â 1 [i]
  26. digital (0, 1, 33)-net over F₃₂ (see above)
  27. digital (0, 1, 33)-net over F₃₂ (see above)
  28. digital (0, 1, 33)-net over F₃₂ (see above)
  29. digital (0, 2, 33)-net over F₃₂, using
    - kÂ =Â 2 construction [i]
  30. digital (0, 2, 33)-net over F₃₂ (see above)
  31. digital (0, 4, 33)-net over F₃₂, using
    - net from sequence [i] based on digital (0, 32)-sequence over F₃₂, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 0 and N(F) ≥ 33, using
        the rational function field F₃₂(x) [i]
      - Niederreiter sequence [i]
  32. digital (0, 8, 33)-net over F₃₂, using
    - net from sequence [i] based on digital (0, 32)-sequence over F₃₂ (see above)
digital (60, 76, 1048575)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32⁷⁶, 1048575, F₃₂, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
  - OA 8-folding and stacking [i] based on linear OA(32⁷⁶, 8388600, F₃₂, 16) (dual of [8388600, 8388524, 17]-code), using
    - discarding factors / shortening the dual code based on linear OA(32⁷⁶, large, F₃₂, 16) (dual of [large, large−76, 17]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 33554431Â = 32⁵âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.