MinT - Information on Result #1842151

Information on Result #1842151

(50, 78, 4702)-net in base 128, using net defined by OOA based on OOA(128⁷⁸, 4702, S₁₂₈, 30, 28), using

OOA 7-folding and stacking with additional row [i] based on OOA(128⁷⁸, 32915, S₁₂₈, 2, 28), using
- discarding factors based on OOA(128⁷⁸, 32919, S₁₂₈, 2, 28), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(128¹⁵, 150, F₁₂₈, 2, 14) (dual of [(150, 2), 285, 15]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,285P) [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
        a function field by SÃ©mirat [i]
    2. OOA(128⁶³, 32769, S₁₂₈, 2, 28), using
      - OOA 2-folding [i] based on OA(128⁶³, 65538, S₁₂₈, 28), using
        discarding parts of the base [i] based on linear OA(256⁵⁵, 65538, F₂₅₆, 28) (dual of [65538, 65483, 29]-code), using
        constructionÂ X applied to C_e(27) âŠ‚ C_e(26) [i] based on
        linear OA(256⁵⁵, 65536, F₂₅₆, 28) (dual of [65536, 65481, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
        linear OA(256⁵³, 65536, F₂₅₆, 27) (dual of [65536, 65483, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [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.