MinT - Information on Result #1189068

Information on Result #1189068

Digital (121, 137, 1048588)-net over F₅, using net defined by OOA based on linear OOA(5¹³⁷, 1048588, F₅, 18, 16) (dual of [(1048588, 18), 18874447, 17]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(5¹³⁷, 4194353, F₅, 2, 16) (dual of [(4194353, 2), 8388569, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(5¹⁶, 52, F₅, 2, 8) (dual of [(52, 2), 88, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (8, 16, 52)-net over F₅, using
      - trace code for nets [i] based on digital (0, 8, 26)-net over F₂₅, using
        net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
        the rational function field F₂₅(x) [i]
        Niederreiter sequence [i]
  2. linear OOA(5¹²¹, 4194301, F₅, 2, 16) (dual of [(4194301, 2), 8388481, 17]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(5¹²¹, 8388602, F₅, 16) (dual of [8388602, 8388481, 17]-code), using
      - discarding factors / shortening the dual code based on linear OA(5¹²¹, large, F₅, 16) (dual of [large, large−121, 17]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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.