MinT - Information on Result #1792043

Information on Result #1792043

Digital (30, 51, 260)-net over F₈, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(8⁵¹, 260, F₈, 21) (dual of [260, 209, 22]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(8⁵⁰, 258, F₈, 21) (dual of [258, 208, 22]-code), using
  - trace code [i] based on linear OA(64²⁵, 129, F₆₄, 21) (dual of [129, 104, 22]-code), using
    - extended algebraic-geometric code AG_e(F,107P) [i] based on function field F/F₆₄ with g(F) = 4 and N(F) ≥ 129, using
      - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₆₄ [i]
2. linear OA(8⁵⁰, 259, F₈, 20) (dual of [259, 209, 21]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 8⁵⁰Â > V_b^sâˆ’1(kâˆ’1)Â = 318 049696 282331 499963 882546 383698 991672 378816 [i]
3. linear OA(8⁰, 1, F₈, 0) (dual of [1, 1, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
    - OA with only one run / dual of code without redundancy [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.