MinT - Information on Result #1812611

Information on Result #1812611

Digital (21, 52, 372)-net over F₈₁, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(81⁵², 372, F₈₁, 3, 31) (dual of [(372, 3), 1064, 32]-NRT-code), using

strength reduction [i] based on linear OOA(81⁵², 372, F₈₁, 3, 32) (dual of [(372, 3), 1064, 33]-NRT-code), using
- constructionÂ X applied to AG(3;F,1074P) âŠ‚ AG(3;F,1079P) [i] based on
  1. linear OOA(81⁴⁸, 369, F₈₁, 3, 32) (dual of [(369, 3), 1059, 33]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1074P) [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, 3, 27) (dual of [(369, 3), 1064, 28]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1079P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370 (see above)
  3. linear OOA(81⁴, 3, F₈₁, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81⁴, 81, F₈₁, 3, 4) (dual of [(81, 3), 239, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;239,81) [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.