MinT - Information on Result #1806785

Information on Result #1806785

Digital (31, 74, 209)-net over F₂₇, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(27⁷⁴, 209, F₂₇, 2, 43) (dual of [(209, 2), 344, 44]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(27⁷⁴, 214, F₂₇, 2, 43) (dual of [(214, 2), 354, 44]-NRT-code), using
- constructionÂ X applied to AG(2;F,370P) âŠ‚ AG(2;F,378P) [i] based on
  1. linear OOA(27⁶⁷, 207, F₂₇, 2, 43) (dual of [(207, 2), 347, 44]-NRT-code), using algebraic-geometric NRT-code AG(2;F,370P) [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(27⁵⁹, 207, F₂₇, 2, 35) (dual of [(207, 2), 355, 36]-NRT-code), using algebraic-geometric NRT-code AG(2;F,378P) [i] based on function field F/F₂₇ with g(F) = 24 and N(F) ≥ 208 (see above)
  3. linear OOA(27⁷, 7, F₂₇, 2, 7) (dual of [(7, 2), 7, 8]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(27⁷, 27, F₂₇, 2, 7) (dual of [(27, 2), 47, 8]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;47,27) [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.