MinT - Information on Result #1230593

Information on Result #1230593

Digital (95, 110, 2400854)-net over F₁₆, using (u,Â u+v)-construction based on

digital (17, 24, 4112)-net over F₁₆, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (0, 0, 257)-net over F₁₆, using
    - s-reduction based on digital (0, 0, s)-net over F₁₆ for arbitrarily large s, using
      - arbitrary set of 16⁰ points [i]
  2. digital (0, 0, 257)-net over F₁₆ (see above)
  3. digital (0, 0, 257)-net over F₁₆ (see above)
  4. digital (0, 0, 257)-net over F₁₆ (see above)
  5. digital (0, 0, 257)-net over F₁₆ (see above)
  6. digital (0, 0, 257)-net over F₁₆ (see above)
  7. digital (0, 0, 257)-net over F₁₆ (see above)
  8. digital (0, 0, 257)-net over F₁₆ (see above)
  9. digital (0, 0, 257)-net over F₁₆ (see above)
  10. digital (0, 1, 257)-net over F₁₆, using
    - s-reduction based on digital (0, 1, s)-net over F₁₆ for arbitrarily large s, using
      - construction for strength kÂ =Â 1 [i]
  11. digital (0, 1, 257)-net over F₁₆ (see above)
  12. digital (0, 1, 257)-net over F₁₆ (see above)
  13. digital (0, 1, 257)-net over F₁₆ (see above)
  14. digital (1, 3, 257)-net over F₁₆, using
    - s-reduction based on digital (1, 3, 273)-net over F₁₆, using
      - kÂ =Â 2 construction [i]
  15. digital (1, 4, 257)-net over F₁₆, using
    - net defined by OOA [i] based on linear OOA(16⁴, 257, F₁₆, 3, 3) (dual of [(257, 3), 767, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(16⁴, 257, F₁₆, 2, 3) (dual of [(257, 2), 510, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(16⁴, 257, F₁₆, 3) (dual of [257, 253, 4]-code or 257-cap in PG(3,16)), using
        ovoid in PG(3,Â 16) [i]
  16. digital (6, 13, 257)-net over F₁₆, using
    - base reduction for projective spaces (embedding PG(6,256) in PG(12,16)) for nets [i] based on digital (0, 7, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]
digital (71, 86, 2396742)-net over F₁₆, using
- trace code for nets [i] based on digital (28, 43, 1198371)-net over F₂₅₆, using
  - net defined by OOA [i] based on linear OOA(256⁴³, 1198371, F₂₅₆, 15, 15) (dual of [(1198371, 15), 17975522, 16]-NRT-code), using
    - OOA 7-folding and stacking with additional row [i] based on linear OA(256⁴³, 8388598, F₂₅₆, 15) (dual of [8388598, 8388555, 16]-code), using
      - discarding factors / shortening the dual code based on linear OA(256⁴³, large, F₂₅₆, 15) (dual of [large, large−43, 16]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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.