MinT - Information on Result #1194242

Information on Result #1194242

Digital (66, 86, 5905)-net over F₉, using net defined by OOA based on linear OOA(9⁸⁶, 5905, F₉, 20, 20) (dual of [(5905, 20), 118014, 21]-NRT-code), using

OA 10-folding and stacking [i] based on linear OA(9⁸⁶, 59050, F₉, 20) (dual of [59050, 58964, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(9⁸⁶, 59054, F₉, 20) (dual of [59054, 58968, 21]-code), using
  - constructionÂ X applied to C_e(19) âŠ‚ C_e(18) [i] based on
    1. linear OA(9⁸⁶, 59049, F₉, 20) (dual of [59049, 58963, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
    2. linear OA(9⁸¹, 59049, F₉, 19) (dual of [59049, 58968, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    3. linear OA(9⁰, 5, F₉, 0) (dual of [5, 5, 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 (67, 87, 5905)-net over F₉	[i]	Net Duplication
2	Digital (68, 88, 5905)-net over F₉	[i]	Net Duplication
3	Digital (76, 96, 5915)-net over F₉	[i]	(u,Â u+v)-Construction for Nets
4	Digital (77, 97, 5921)-net over F₉	[i]
5	Digital (78, 98, 5925)-net over F₉	[i]
6	Digital (79, 99, 5933)-net over F₉	[i]
7	Digital (80, 100, 5935)-net over F₉	[i]
8	Digital (81, 101, 5937)-net over F₉	[i]
9	Digital (82, 102, 5939)-net over F₉	[i]