MinT - Information on Result #1208182

Information on Result #1208182

Digital (200, 213, 5592453)-net over F₃, using (u,Â u+v)-construction based on

digital (11, 17, 53)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3¹⁷, 53, F₃, 6, 6) (dual of [(53, 6), 301, 7]-NRT-code), using
  - appending kth column [i] based on linear OOA(3¹⁷, 53, F₃, 5, 6) (dual of [(53, 5), 248, 7]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(3⁵, 20, F₃, 5, 3) (dual of [(20, 5), 95, 4]-NRT-code), using
        appending 2 arbitrary columns [i] based on linear OOA(3⁵, 20, F₃, 3, 3) (dual of [(20, 3), 55, 4]-NRT-code), using
        appending kth column [i] based on linear OOA(3⁵, 20, F₃, 2, 3) (dual of [(20, 2), 35, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁵, 20, F₃, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,3)), using
        doubling the cap [i] based on linear OA(3⁴, 10, F₃, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
        ovoid in PG(3,Â 3) [i]
      2. linear OOA(3¹², 33, F₃, 5, 6) (dual of [(33, 5), 153, 7]-NRT-code), using
        extracting embedded OOA [i] based on digital (6, 12, 33)-net over F₃, using
        linear code embedding found in a computer search [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(3²¹³, 5592453, F₃, 5, 13) (dual of [(5592453, 5), 27962052, 14]-NRT-code)	[i]		Extracting Embedded OOA