MinT - Information on Result #895262

Information on Result #895262

Linear OOA(3²⁰⁵, 4194357, F₃, 2, 19) (dual of [(4194357, 2), 8388509, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²⁴, 56, F₃, 2, 9) (dual of [(56, 2), 88, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (15, 24, 56)-net over F₃, using
  - trace code for nets [i] based on digital (3, 12, 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]
linear OOA(3¹⁸¹, 4194301, F₃, 2, 19) (dual of [(4194301, 2), 8388421, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁸¹, 8388602, F₃, 19) (dual of [8388602, 8388421, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸¹, large, F₃, 19) (dual of [large, large−181, 20]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3²⁰⁵, 4194357, F₃, 2, 18) (dual of [(4194357, 2), 8388509, 19]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3²⁰⁶, 4194357, F₃, 2, 19) (dual of [(4194357, 2), 8388508, 20]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3²⁰⁵, 3845767, F₃, 3, 19) (dual of [(3845767, 3), 11537096, 20]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(3²⁰⁵, 3845767, F₃, 4, 19) (dual of [(3845767, 4), 15382863, 20]-NRT-code)	[i]
5	Linear OOA(3²⁰⁵, 3845767, F₃, 5, 19) (dual of [(3845767, 5), 19228630, 20]-NRT-code)	[i]
6	Digital (186, 205, 3845767)-net over F₃	[i]
7	Linear OOA(3²⁰⁵, 2097178, F₃, 4, 19) (dual of [(2097178, 4), 8388507, 20]-NRT-code)	[i]	OOA Folding