MinT - Information on Result #1811849

Information on Result #1811849

Digital (34, 79, 516)-net over F₆₄, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(64⁷⁹, 516, F₆₄, 2, 45) (dual of [(516, 2), 953, 46]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(64⁷⁹, 518, F₆₄, 2, 45) (dual of [(518, 2), 957, 46]-NRT-code), using
- constructionÂ X applied to AG(2;F,978P) âŠ‚ AG(2;F,985P) [i] based on
  1. linear OOA(64⁷³, 512, F₆₄, 2, 45) (dual of [(512, 2), 951, 46]-NRT-code), using algebraic-geometric NRT-code AG(2;F,978P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
    - the Hermitian function field over F₆₄ [i]
  2. linear OOA(64⁶⁶, 512, F₆₄, 2, 38) (dual of [(512, 2), 958, 39]-NRT-code), using algebraic-geometric NRT-code AG(2;F,985P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (see above)
  3. linear OOA(64⁶, 6, F₆₄, 2, 6) (dual of [(6, 2), 6, 7]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁶, 64, F₆₄, 2, 6) (dual of [(64, 2), 122, 7]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;122,64) [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.