MinT - Information on Result #1791893

Information on Result #1791893

Digital (18, 40, 67)-net over F₈, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(8⁴⁰, 67, F₈, 3, 22) (dual of [(67, 3), 161, 23]-NRT-code), using

constructionÂ X applied to AG(3;F,169P) âŠ‚ AG(3;F,174P) [i] based on
1. linear OOA(8³⁶, 64, F₈, 3, 22) (dual of [(64, 3), 156, 23]-NRT-code), using algebraic-geometric NRT-code AG(3;F,169P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
  - the Suzuki function field over F₈ [i]
2. linear OOA(8³¹, 64, F₈, 3, 17) (dual of [(64, 3), 161, 18]-NRT-code), using algebraic-geometric NRT-code AG(3;F,174P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
3. linear OOA(8⁴, 3, F₈, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8⁴, 8, F₈, 3, 4) (dual of [(8, 3), 20, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;20,8) [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.