MinT - Information on Result #1793768

Information on Result #1793768

Digital (53, 115, 145)-net over F₈, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(8¹¹⁵, 145, F₈, 3, 62) (dual of [(145, 3), 320, 63]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(8¹¹⁵, 148, F₈, 3, 62) (dual of [(148, 3), 329, 63]-NRT-code), using
- strength reduction [i] based on linear OOA(8¹¹⁵, 148, F₈, 3, 63) (dual of [(148, 3), 329, 64]-NRT-code), using
  - constructionÂ X applied to AG(3;F,365P) âŠ‚ AG(3;F,373P) [i] based on
    1. linear OOA(8¹⁰⁸, 143, F₈, 3, 63) (dual of [(143, 3), 321, 64]-NRT-code), using algebraic-geometric NRT-code AG(3;F,365P) [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
      - Drinfeld modules of rank 1 [i]
    2. linear OOA(8¹⁰⁰, 143, F₈, 3, 55) (dual of [(143, 3), 329, 56]-NRT-code), using algebraic-geometric NRT-code AG(3;F,373P) [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144 (see above)
    3. linear OOA(8⁷, 5, F₈, 3, 7) (dual of [(5, 3), 8, 8]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(8⁷, 8, F₈, 3, 7) (dual of [(8, 3), 17, 8]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(3;17,8) [i]

Mode: 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.