MinT - Information on Result #1205088

Information on Result #1205088

Digital (158, 172, 1366566)-net over F₃, using trace code for nets based on digital (72, 86, 683283)-net over F₉, using

net defined by OOA [i] based on linear OOA(9⁸⁶, 683283, F₉, 14, 14) (dual of [(683283, 14), 9565876, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(9⁸⁶, 4782981, F₉, 14) (dual of [4782981, 4782895, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁸⁶, 4782984, F₉, 14) (dual of [4782984, 4782898, 15]-code), using
    - constructionÂ X applied to C_e(13) âŠ‚ C_e(11) [i] based on
      1. linear OA(9⁸⁵, 4782969, F₉, 14) (dual of [4782969, 4782884, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      2. linear OA(9⁷¹, 4782969, F₉, 12) (dual of [4782969, 4782898, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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 (159, 173, 1366566)-net over F₃	[i]		Net Duplication
2	Digital (160, 174, 1366566)-net over F₃	[i]
3	Digital (161, 175, 1366566)-net over F₃	[i]