MinT - Information on Result #1812725

Information on Result #1812725

Digital (23, 58, 372)-net over F₈₁, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(81⁵⁸, 372, F₈₁, 4, 35) (dual of [(372, 4), 1430, 36]-NRT-code), using

strength reduction [i] based on linear OOA(81⁵⁸, 372, F₈₁, 4, 36) (dual of [(372, 4), 1430, 37]-NRT-code), using
- constructionÂ X applied to AG(4;F,1439P) âŠ‚ AG(4;F,1446P) [i] based on
  1. linear OOA(81⁵², 369, F₈₁, 4, 36) (dual of [(369, 4), 1424, 37]-NRT-code), using algebraic-geometric NRT-code AG(4;F,1439P) [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(81⁴⁵, 369, F₈₁, 4, 29) (dual of [(369, 4), 1431, 30]-NRT-code), using algebraic-geometric NRT-code AG(4;F,1446P) [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.