MinT - Information on Result #1789624

Information on Result #1789624

Digital (16, 36, 50)-net over F₇, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(7³⁶, 50, F₇, 2, 20) (dual of [(50, 2), 64, 21]-NRT-code), using

constructionÂ X applied to AG(2;F,73P) âŠ‚ AG(2;F,77P) [i] based on
1. linear OOA(7³³, 47, F₇, 2, 20) (dual of [(47, 2), 61, 21]-NRT-code), using algebraic-geometric NRT-code AG(2;F,73P) [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(7²⁹, 47, F₇, 2, 16) (dual of [(47, 2), 65, 17]-NRT-code), using algebraic-geometric NRT-code AG(2;F,77P) [i] based on function field F/F₇ with g(F) = 13 and N(F) ≥ 48 (see above)
3. linear OOA(7³, 3, F₇, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7³, 7, F₇, 2, 3) (dual of [(7, 2), 11, 4]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;11,7) [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.