MinT - Information on Result #1812010

Information on Result #1812010

Digital (36, 85, 517)-net over F₆₄, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(64⁸⁵, 517, F₆₄, 3, 49) (dual of [(517, 3), 1466, 50]-NRT-code), using

strength reduction [i] based on linear OOA(64⁸⁵, 517, F₆₄, 3, 50) (dual of [(517, 3), 1466, 51]-NRT-code), using
- constructionÂ X applied to AG(3;F,1485P) âŠ‚ AG(3;F,1493P) [i] based on
  1. linear OOA(64⁷⁸, 512, F₆₄, 3, 50) (dual of [(512, 3), 1458, 51]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1485P) [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(64⁷⁰, 512, F₆₄, 3, 42) (dual of [(512, 3), 1466, 43]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1493P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (see above)
  3. linear OOA(64⁷, 5, F₆₄, 3, 7) (dual of [(5, 3), 8, 8]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁷, 64, F₆₄, 3, 7) (dual of [(64, 3), 185, 8]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;185,64) [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.