MinT - Information on Result #3279356

Information on Result #3279356

(107, 124, 2098206)-net in base 16, using 16¹ times duplication based on (106, 123, 2098206)-net in base 16, using

(u,Â u+v)-construction [i] based on
1. (17, 25, 1056)-net in base 16, using
  - base change [i] 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)
2. digital (81, 98, 2097150)-net over F₁₆, using
  - net defined by OOA [i] based on linear OOA(16⁹⁸, 2097150, F₁₆, 18, 17) (dual of [(2097150, 18), 37748602, 18]-NRT-code), using
    - OOA 4-folding and stacking with additional row [i] based on linear OOA(16⁹⁸, 8388601, F₁₆, 2, 17) (dual of [(8388601, 2), 16777104, 18]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(16⁹⁸, 8388602, F₁₆, 2, 17) (dual of [(8388602, 2), 16777106, 18]-NRT-code), using
        trace code [i] based on linear OOA(256⁴⁹, 4194301, F₂₅₆, 2, 17) (dual of [(4194301, 2), 8388553, 18]-NRT-code), using
        OOA 2-folding [i] based on linear OA(256⁴⁹, 8388602, F₂₅₆, 17) (dual of [8388602, 8388553, 18]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁴⁹, large, F₂₅₆, 17) (dual of [large, large−49, 18]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]

Mode: Constructive.

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.