MinT - Information on Result #1184249

Information on Result #1184249

Linear OOA(3¹⁷³, 1048602, F₃, 20, 16) (dual of [(1048602, 20), 20971867, 17]-NRT-code), using OOA 2-folding and stacking with additional row based on linear OOA(3¹⁷³, 2097205, F₃, 4, 16) (dual of [(2097205, 4), 8388647, 17]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁷³, 2097206, F₃, 4, 16) (dual of [(2097206, 4), 8388651, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3²², 56, F₃, 4, 8) (dual of [(56, 4), 202, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (14, 22, 56)-net over F₃, using
      - trace code for nets [i] based on digital (3, 11, 28)-net over F₉, using
        net from sequence [i] based on digital (3, 27)-sequence over F₉, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
        the Hermitian function field over F₉ [i]
  2. linear OOA(3¹⁵¹, 2097150, F₃, 4, 16) (dual of [(2097150, 4), 8388449, 17]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(3¹⁵¹, 8388600, F₃, 16) (dual of [8388600, 8388449, 17]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁵¹, large, F₃, 16) (dual of [large, large−151, 17]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: Constructive and linear.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (157, 173, 1048602)-net over F₃	[i]		Net Defined by OOA