MinT - Information on Result #1208188

Information on Result #1208188

Digital (210, 223, 5592764)-net over F₃, using (u,Â u+v)-construction based on

digital (21, 27, 364)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3²⁷, 364, F₃, 6, 6) (dual of [(364, 6), 2157, 7]-NRT-code), using
  - appending kth column [i] based on linear OOA(3²⁷, 364, F₃, 5, 6) (dual of [(364, 5), 1793, 7]-NRT-code), using
    - OA 3-folding and stacking [i] based on linear OA(3²⁷, 1092, F₃, 6) (dual of [1092, 1065, 7]-code), using
      - 1 times truncation [i] based on linear OA(3²⁸, 1093, F₃, 7) (dual of [1093, 1065, 8]-code), using
        the BCH-code C(I) with length 1093Â | 3⁷âˆ’1, defining interval IÂ =Â {−3,−1,1,…,9}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
digital (183, 196, 5592400)-net over F₃, using
- trace code for nets [i] based on digital (85, 98, 2796200)-net over F₉, using
  - net defined by OOA [i] based on linear OOA(9⁹⁸, 2796200, F₉, 14, 13) (dual of [(2796200, 14), 39146702, 14]-NRT-code), using
    - OOA 3-folding and stacking with additional row [i] based on linear OOA(9⁹⁸, 8388601, F₉, 2, 13) (dual of [(8388601, 2), 16777104, 14]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(9⁹⁸, 8388602, F₉, 2, 13) (dual of [(8388602, 2), 16777106, 14]-NRT-code), using
        trace code [i] based on linear OOA(81⁴⁹, 4194301, F₈₁, 2, 13) (dual of [(4194301, 2), 8388553, 14]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81⁴⁹, 8388602, F₈₁, 13) (dual of [8388602, 8388553, 14]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁴⁹, large, F₈₁, 13) (dual of [large, large−49, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²²³, 5592764, F₃, 5, 13) (dual of [(5592764, 5), 27963597, 14]-NRT-code)	[i]		Extracting Embedded OOA