MinT - Information on Result #1789660

Information on Result #1789660

Digital (17, 39, 50)-net over F₇, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(7³⁹, 50, F₇, 3, 22) (dual of [(50, 3), 111, 23]-NRT-code), using

constructionÂ X applied to AG(3;F,118P) âŠ‚ AG(3;F,123P) [i] based on
1. linear OOA(7³⁵, 47, F₇, 3, 22) (dual of [(47, 3), 106, 23]-NRT-code), using algebraic-geometric NRT-code AG(3;F,118P) [i] based on function field F/F₇ with g(F) = 13 and N(F) ≥ 48, using
  - an algebraic function field by Teo [i]
2. linear OOA(7³⁰, 47, F₇, 3, 17) (dual of [(47, 3), 111, 18]-NRT-code), using algebraic-geometric NRT-code AG(3;F,123P) [i] based on function field F/F₇ with g(F) = 13 and N(F) ≥ 48 (see above)
3. linear OOA(7⁴, 3, F₇, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7⁴, 7, F₇, 3, 4) (dual of [(7, 3), 17, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;17,7) [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.