MinT - Information on Result #1806705

Information on Result #1806705

Digital (30, 71, 211)-net over F₂₇, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(27⁷¹, 211, F₂₇, 2, 41) (dual of [(211, 2), 351, 42]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(27⁷¹, 213, F₂₇, 2, 41) (dual of [(213, 2), 355, 42]-NRT-code), using
- constructionÂ X applied to AG(2;F,372P) âŠ‚ AG(2;F,379P) [i] based on
  1. linear OOA(27⁶⁵, 207, F₂₇, 2, 41) (dual of [(207, 2), 349, 42]-NRT-code), using algebraic-geometric NRT-code AG(2;F,372P) [i] based on function field F/F₂₇ with g(F) = 24 and N(F) ≥ 208, using
    - an algebraic function field by Beelen and Pellikaan [i]
  2. linear OOA(27⁵⁸, 207, F₂₇, 2, 34) (dual of [(207, 2), 356, 35]-NRT-code), using algebraic-geometric NRT-code AG(2;F,379P) [i] based on function field F/F₂₇ with g(F) = 24 and N(F) ≥ 208 (see above)
  3. linear OOA(27⁶, 6, F₂₇, 2, 6) (dual of [(6, 2), 6, 7]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(27⁶, 27, F₂₇, 2, 6) (dual of [(27, 2), 48, 7]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;48,27) [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.