MinT - Information on Result #1753338

Information on Result #1753338

Digital (156, 171, 1479377)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁷¹, 1479377, F₂, 5, 15) (dual of [(1479377, 5), 7396714, 16]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁷¹, 1677726, F₂, 5, 15) (dual of [(1677726, 5), 8388459, 16]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁹, 6, F₂, 5, 7) (dual of [(6, 5), 21, 8]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(5;F,22P) [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(2¹⁶², 1677720, F₂, 5, 15) (dual of [(1677720, 5), 8388438, 16]-NRT-code), using
    - OOA 5-folding [i] based on linear OA(2¹⁶², 8388600, F₂, 15) (dual of [8388600, 8388438, 16]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁶², large, F₂, 15) (dual of [large, large−162, 16]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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.