MinT - Information on Result #895151

Information on Result #895151

Linear OOA(3¹⁶⁹, 4194333, F₃, 2, 16) (dual of [(4194333, 2), 8388497, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁸, 32, F₃, 2, 8) (dual of [(32, 2), 46, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (10, 18, 32)-net over F₃, using
  - trace code for nets [i] based on digital (1, 9, 16)-net over F₉, using
    - net from sequence [i] based on digital (1, 15)-sequence over F₉, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
        a function field by GarcÃa and Quoos [i]
linear OOA(3¹⁵¹, 4194301, F₃, 2, 16) (dual of [(4194301, 2), 8388451, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁵¹, 8388602, F₃, 16) (dual of [8388602, 8388451, 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.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3¹⁷⁰, 4194333, F₃, 2, 16) (dual of [(4194333, 2), 8388496, 17]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3¹⁶⁹, 3815468, F₃, 3, 16) (dual of [(3815468, 3), 11446235, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(3¹⁶⁹, 3815468, F₃, 4, 16) (dual of [(3815468, 4), 15261703, 17]-NRT-code)	[i]
4	Linear OOA(3¹⁶⁹, 3815468, F₃, 5, 16) (dual of [(3815468, 5), 19077171, 17]-NRT-code)	[i]
5	Digital (153, 169, 3815468)-net over F₃	[i]
6	Linear OOA(3¹⁶⁹, 2097166, F₃, 4, 16) (dual of [(2097166, 4), 8388495, 17]-NRT-code)	[i]	OOA Folding