MinT - Information on Result #1844122

Information on Result #1844122

(28, 44, 8321)-net in base 128, using (u,Â u+v)-construction based on

digital (0, 8, 129)-net over F₁₂₈, using
- net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 0 and N(F) ≥ 129, using
    - the rational function field F₁₂₈(x) [i]
  - Niederreiter sequence [i]
(20, 36, 8192)-net in base 128, using
- net defined by OOA [i] based on OOA(128³⁶, 8192, S₁₂₈, 16, 16), using
  - OA 8-folding and stacking [i] based on OA(128³⁶, 65536, S₁₂₈, 16), using
    - discarding factors based on OA(128³⁶, 65538, S₁₂₈, 16), using
      - discarding parts of the base [i] based on linear OA(256³¹, 65538, F₂₅₆, 16) (dual of [65538, 65507, 17]-code), using
        constructionÂ X applied to C_e(15) âŠ‚ C_e(14) [i] based on
        linear OA(256³¹, 65536, F₂₅₆, 16) (dual of [65536, 65505, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
        linear OA(256²⁹, 65536, F₂₅₆, 15) (dual of [65536, 65507, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
        linear OA(256⁰, 2, F₂₅₆, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁰, s, F₂₅₆, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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.