MinT - Information on Result #1797360

Information on Result #1797360

Digital (18, 31, 238)-net over F₉, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(9³¹, 238, F₉, 13) (dual of [238, 207, 14]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(9³⁰, 236, F₉, 13) (dual of [236, 206, 14]-code), using
  - trace code [i] based on linear OA(81¹⁵, 118, F₈₁, 13) (dual of [118, 103, 14]-code), using
    - extended algebraic-geometric code AG_e(F,104P) [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 118, using
      - sharp bound on the number of rational points on curves with genus 2 [i]
2. linear OA(9³⁰, 237, F₉, 12) (dual of [237, 207, 13]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 9³⁰Â > V_b^sâˆ’1(kâˆ’1)Â = 21615 586080 098392 378378 716129 [i]
3. linear OA(9⁰, 1, F₉, 0) (dual of [1, 1, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 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.