MinT - Information on Result #1785838

Information on Result #1785838

Digital (27, 58, 56)-net over F₅, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(5⁵⁸, 56, F₅, 3, 31) (dual of [(56, 3), 110, 32]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(5⁵⁸, 57, F₅, 3, 31) (dual of [(57, 3), 113, 32]-NRT-code), using
- constructionÂ X applied to AG(3;F,130P) âŠ‚ AG(3;F,135P) [i] based on
  1. linear OOA(5⁵⁴, 54, F₅, 3, 31) (dual of [(54, 3), 108, 32]-NRT-code), using algebraic-geometric NRT-code AG(3;F,130P) [i] based on function field F/F₅ with g(F) = 23 and N(F) ≥ 55, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]
  2. linear OOA(5⁴⁹, 54, F₅, 3, 26) (dual of [(54, 3), 113, 27]-NRT-code), using algebraic-geometric NRT-code AG(3;F,135P) [i] based on function field F/F₅ with g(F) = 23 and N(F) ≥ 55 (see above)
  3. linear OOA(5⁴, 3, F₅, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(5⁴, 5, F₅, 3, 4) (dual of [(5, 3), 11, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;11,5) [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.