MinT - Information on Result #1193884

Information on Result #1193884

Digital (77, 92, 683282)-net over F₉, using net defined by OOA based on linear OOA(9⁹², 683282, F₉, 15, 15) (dual of [(683282, 15), 10249138, 16]-NRT-code), using

OOA 7-folding and stacking with additional row [i] based on linear OA(9⁹², 4782975, F₉, 15) (dual of [4782975, 4782883, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(9⁹², 4782976, F₉, 15) (dual of [4782976, 4782884, 16]-code), using
  - constructionÂ X applied to C_e(14) âŠ‚ C_e(13) [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(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]
    3. linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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		Method
1	Digital (169, 184, 1366564)-net over F₃	[i]	Trace Code for Nets
2	Digital (84, 99, 683292)-net over F₉	[i]	(u,Â u+v)-Construction for Nets
3	Digital (85, 100, 683298)-net over F₉	[i]
4	Digital (86, 101, 683302)-net over F₉	[i]
5	Digital (87, 102, 683310)-net over F₉	[i]
6	Digital (88, 103, 683312)-net over F₉	[i]
7	Digital (89, 104, 683314)-net over F₉	[i]
8	(89, 104, 683320)-net in base 9	[i]