MinT - Information on Result #1808762

Information on Result #1808762

Digital (27, 64, 226)-net over F₃₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(32⁶⁴, 226, F₃₂, 2, 37) (dual of [(226, 2), 388, 38]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(32⁶⁴, 227, F₃₂, 2, 37) (dual of [(227, 2), 390, 38]-NRT-code), using
- constructionÂ X applied to AG(2;F,410P) âŠ‚ AG(2;F,414P) [i] based on
  1. linear OOA(32⁶¹, 224, F₃₂, 2, 37) (dual of [(224, 2), 387, 38]-NRT-code), using algebraic-geometric NRT-code AG(2;F,410P) [i] based on function field F/F₃₂ with g(F) = 24 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]
  2. linear OOA(32⁵⁷, 224, F₃₂, 2, 33) (dual of [(224, 2), 391, 34]-NRT-code), using algebraic-geometric NRT-code AG(2;F,414P) [i] based on function field F/F₃₂ with g(F) = 24 and N(F) ≥ 225 (see above)
  3. linear OOA(32³, 3, F₃₂, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(32³, 32, F₃₂, 2, 3) (dual of [(32, 2), 61, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;61,32) [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.