MinT - Information on Result #1812685

Information on Result #1812685

Digital (22, 56, 372)-net over F₈₁, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(81⁵⁶, 372, F₈₁, 4, 34) (dual of [(372, 4), 1432, 35]-NRT-code), using

constructionÂ X applied to AG(4;F,1441P) âŠ‚ AG(4;F,1448P) [i] based on
1. linear OOA(81⁵⁰, 369, F₈₁, 4, 34) (dual of [(369, 4), 1426, 35]-NRT-code), using algebraic-geometric NRT-code AG(4;F,1441P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
  - a function field by GarcÃa and Quoos [i]
2. linear OOA(81⁴³, 369, F₈₁, 4, 27) (dual of [(369, 4), 1433, 28]-NRT-code), using algebraic-geometric NRT-code AG(4;F,1448P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370 (see above)
3. linear OOA(81⁶, 3, F₈₁, 4, 6) (dual of [(3, 4), 6, 7]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(81⁶, 81, F₈₁, 4, 6) (dual of [(81, 4), 318, 7]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(4;318,81) [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.