MinT - Information on Result #1648141

Information on Result #1648141

Linear OOA(3²⁰⁰, 2796227, F₃, 5, 19) (dual of [(2796227, 5), 13980935, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁰⁰, 2796227, F₃, 3, 19) (dual of [(2796227, 3), 8388481, 20]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3¹⁹, 26, F₃, 3, 9) (dual of [(26, 3), 59, 10]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(3⁶, 14, F₃, 3, 4) (dual of [(14, 3), 36, 5]-NRT-code), using
      - extracting embedded OOA [i] based on digital (2, 6, 14)-net over F₃, using
        linear code embedding found in a computer search [i]
    2. linear OOA(3¹³, 13, F₃, 3, 9) (dual of [(13, 3), 26, 10]-NRT-code), using
      - extracting embedded OOA [i] based on digital (4, 13, 13)-net over F₃, using
        a shift-net [i]
2. linear OOA(3¹⁸¹, 2796201, F₃, 3, 19) (dual of [(2796201, 3), 8388422, 20]-NRT-code), using
  - OOA 3-folding [i] 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: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²⁰⁰, 1398113, F₃, 25, 19) (dual of [(1398113, 25), 34952625, 20]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row