MinT - Information on Result #1841123

Information on Result #1841123

(76, 97, 209724)-net in base 32, using net defined by OOA based on OOA(32⁹⁷, 209724, S₃₂, 22, 21), using

OOA 5-folding and stacking with additional row [i] based on OOA(32⁹⁷, 1048621, S₃₂, 2, 21), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(32¹¹, 44, F₃₂, 2, 10) (dual of [(44, 2), 77, 11]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,77P) [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
      - a function field by SÃ©mirat [i]
  2. OOA(32⁸⁶, 1048577, S₃₂, 2, 21), using
    - OOA 2-folding [i] based on OA(32⁸⁶, 2097154, S₃₂, 21), using
      - discarding factors based on OA(32⁸⁶, 2097155, S₃₂, 21), using
        discarding parts of the base [i] based on linear OA(128⁶¹, 2097155, F₁₂₈, 21) (dual of [2097155, 2097094, 22]-code), using
        constructionÂ X applied to C_e(20) âŠ‚ C_e(19) [i] based on
        linear OA(128⁶¹, 2097152, F₁₂₈, 21) (dual of [2097152, 2097091, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
        linear OA(128⁵⁸, 2097152, F₁₂₈, 20) (dual of [2097152, 2097094, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
        linear OA(128⁰, 3, F₁₂₈, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 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.