MinT - Information on Result #1181282

Information on Result #1181282

Digital (18, 35, 18)-net over F₂, using net defined by OOA based on linear OOA(2³⁵, 18, F₂, 24, 17) (dual of [(18, 24), 397, 18]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(2³⁵, 19, F₂, 8, 17) (dual of [(19, 8), 117, 18]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹², 9, F₂, 8, 8) (dual of [(9, 8), 60, 9]-NRT-code), using
    - appending kth column [i] based on linear OOA(2¹², 9, F₂, 7, 8) (dual of [(9, 7), 51, 9]-NRT-code), using
      - extracting embedded OOA [i] based on digital (4, 12, 9)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2²³, 10, F₂, 8, 17) (dual of [(10, 8), 57, 18]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(8;F,62P) [i] based on function field F/F₂ with g(F) = 6 and N(F) ≥ 10, using
      - an explicitly constructive algebraic function field [i]

Mode: Constructive and 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.