MinT - Information on Result #1789546

Information on Result #1789546

Digital (12, 28, 40)-net over F₇, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(7²⁸, 40, F₇, 2, 16) (dual of [(40, 2), 52, 17]-NRT-code), using

constructionÂ X applied to AG(2;F,57P) âŠ‚ AG(2;F,61P) [i] based on
1. linear OOA(7²⁵, 37, F₇, 2, 16) (dual of [(37, 2), 49, 17]-NRT-code), using algebraic-geometric NRT-code AG(2;F,57P) [i] based on function field F/F₇ with g(F) = 9 and N(F) ≥ 38, using
  - an algebraic function field over â„¤₇ by Yeo [i]
2. linear OOA(7²¹, 37, F₇, 2, 12) (dual of [(37, 2), 53, 13]-NRT-code), using algebraic-geometric NRT-code AG(2;F,61P) [i] based on function field F/F₇ with g(F) = 9 and N(F) ≥ 38 (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.