MinT - Information on Result #1809417

Information on Result #1809417

Digital (37, 88, 277)-net over F₃₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(32⁸⁸, 277, F₃₂, 2, 51) (dual of [(277, 2), 466, 52]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(32⁸⁸, 279, F₃₂, 2, 51) (dual of [(279, 2), 470, 52]-NRT-code), using
- constructionÂ X applied to AG(2;F,492P) âŠ‚ AG(2;F,500P) [i] based on
  1. linear OOA(32⁸¹, 272, F₃₂, 2, 51) (dual of [(272, 2), 463, 52]-NRT-code), using algebraic-geometric NRT-code AG(2;F,492P) [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]
  2. linear OOA(32⁷³, 272, F₃₂, 2, 43) (dual of [(272, 2), 471, 44]-NRT-code), using algebraic-geometric NRT-code AG(2;F,500P) [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273 (see above)
  3. linear OOA(32⁷, 7, F₃₂, 2, 7) (dual of [(7, 2), 7, 8]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(32⁷, 32, F₃₂, 2, 7) (dual of [(32, 2), 57, 8]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;57,32) [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.