MinT - Information on Result #1183259

Information on Result #1183259

Linear OOA(3¹⁰⁹, 1678004, F₃, 15, 10) (dual of [(1678004, 15), 25169951, 11]-NRT-code), using OOA stacking with additional row based on linear OOA(3¹⁰⁹, 1678005, F₃, 5, 10) (dual of [(1678005, 5), 8389916, 11]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3¹⁸, 285, F₃, 5, 5) (dual of [(285, 5), 1407, 6]-NRT-code), using
  - appending kth column [i] based on linear OOA(3¹⁸, 285, F₃, 4, 5) (dual of [(285, 4), 1122, 6]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(3¹, 95, F₃, 4, 1) (dual of [(95, 4), 379, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(3¹, s, F₃, 4, 1) for arbitrarily large s, using
        appending 3 arbitrary columns [i] based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      2. linear OOA(3⁵, 95, F₃, 4, 2) (dual of [(95, 4), 375, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(3⁵, 121, F₃, 4, 2) (dual of [(121, 4), 479, 3]-NRT-code), using
        appending 2 arbitrary columns [i] based on linear OOA(3⁵, 121, F₃, 2, 2) (dual of [(121, 2), 237, 3]-NRT-code), using
        appending kth column [i] based on linear OA(3⁵, 121, F₃, 2) (dual of [121, 116, 3]-code), using
        Hamming code H(5,3) [i]
      3. linear OOA(3¹², 95, F₃, 4, 5) (dual of [(95, 4), 368, 6]-NRT-code), using
        extracting embedded OOA [i] based on digital (7, 12, 95)-net over F₃, using
        linear code embedding found in a computer search [i]
2. linear OOA(3⁹¹, 1677720, F₃, 5, 10) (dual of [(1677720, 5), 8388509, 11]-NRT-code), using
  - OOA 5-folding [i] based on linear OA(3⁹¹, 8388600, F₃, 10) (dual of [8388600, 8388509, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁹¹, large, F₃, 10) (dual of [large, large−91, 11]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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 (99, 109, 1678004)-net over F₃	[i]		Net Defined by OOA