MinT - Information on Result #1772937

Information on Result #1772937

Digital (30, 60, 56)-net over F₄, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4⁶⁰, 56, F₄, 3, 30) (dual of [(56, 3), 108, 31]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4⁶⁰, 57, F₄, 3, 30) (dual of [(57, 3), 111, 31]-NRT-code), using
- constructionÂ X applied to AG(3;F,131P) âŠ‚ AG(3;F,136P) [i] based on
  1. linear OOA(4⁵⁶, 54, F₄, 3, 30) (dual of [(54, 3), 106, 31]-NRT-code), using algebraic-geometric NRT-code AG(3;F,131P) [i] based on function field F/F₄ with g(F) = 26 and N(F) ≥ 55, using
    - Drinfeld modules of rank 1 [i]
  2. linear OOA(4⁵¹, 54, F₄, 3, 25) (dual of [(54, 3), 111, 26]-NRT-code), using algebraic-geometric NRT-code AG(3;F,136P) [i] based on function field F/F₄ with g(F) = 26 and N(F) ≥ 55 (see above)
  3. linear OOA(4⁴, 3, F₄, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4⁴, 4, F₄, 3, 4) (dual of [(4, 3), 8, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;8,4) [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.