MinT - Information on Result #1205103

Information on Result #1205103

Digital (171, 186, 1366566)-net over F₃, using trace code for nets based on digital (78, 93, 683283)-net over F₉, using

net defined by OOA [i] based on linear OOA(9⁹³, 683283, F₉, 15, 15) (dual of [(683283, 15), 10249152, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(9⁹³, 4782982, F₉, 15) (dual of [4782982, 4782889, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁹³, 4782984, F₉, 15) (dual of [4782984, 4782891, 16]-code), using
    - constructionÂ X applied to C_e(14) âŠ‚ C_e(12) [i] based on
      1. linear OA(9⁹², 4782969, F₉, 15) (dual of [4782969, 4782877, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
      2. linear OA(9⁷⁸, 4782969, F₉, 13) (dual of [4782969, 4782891, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      3. linear OA(9¹, 15, F₉, 1) (dual of [15, 14, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(9¹, s, F₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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	Digital (172, 187, 1366566)-net over F₃	[i]		Net Duplication
2	Digital (173, 188, 1366566)-net over F₃	[i]
3	Digital (174, 189, 1366566)-net over F₃	[i]