MinT - Information on Result #1807879

Information on Result #1807879

Digital (45, 107, 281)-net over F₂₇, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(27¹⁰⁷, 281, F₂₇, 2, 62) (dual of [(281, 2), 455, 63]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(27¹⁰⁷, 282, F₂₇, 2, 62) (dual of [(282, 2), 457, 63]-NRT-code), using
- constructionÂ X applied to AG(2;F,495P) âŠ‚ AG(2;F,499P) [i] based on
  1. linear OOA(27¹⁰⁴, 279, F₂₇, 2, 62) (dual of [(279, 2), 454, 63]-NRT-code), using algebraic-geometric NRT-code AG(2;F,495P) [i] based on function field F/F₂₇ with g(F) = 42 and N(F) ≥ 280, using
    - Drinfeld modules of rank 1 [i]
  2. linear OOA(27¹⁰⁰, 279, F₂₇, 2, 58) (dual of [(279, 2), 458, 59]-NRT-code), using algebraic-geometric NRT-code AG(2;F,499P) [i] based on function field F/F₂₇ with g(F) = 42 and N(F) ≥ 280 (see above)
  3. linear OOA(27³, 3, F₂₇, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(27³, 27, F₂₇, 2, 3) (dual of [(27, 2), 51, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;51,27) [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.