MinT - Information on Result #1194308

Information on Result #1194308

Digital (70, 91, 5905)-net over F₉, using net defined by OOA based on linear OOA(9⁹¹, 5905, F₉, 21, 21) (dual of [(5905, 21), 123914, 22]-NRT-code), using

OOA 10-folding and stacking with additional row [i] based on linear OA(9⁹¹, 59051, F₉, 21) (dual of [59051, 58960, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(9⁹¹, 59054, F₉, 21) (dual of [59054, 58963, 22]-code), using
  - constructionÂ X applied to C_e(20) âŠ‚ C_e(19) [i] based on
    1. linear OA(9⁹¹, 59049, F₉, 21) (dual of [59049, 58958, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    2. 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]
    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 (80, 101, 5915)-net over F₉	[i]	(u,Â u+v)-Construction for Nets
2	Digital (81, 102, 5921)-net over F₉	[i]
3	Digital (82, 103, 5925)-net over F₉	[i]
4	Digital (83, 104, 5933)-net over F₉	[i]
5	Digital (84, 105, 5935)-net over F₉	[i]
6	Digital (85, 106, 5937)-net over F₉	[i]
7	Digital (86, 107, 5939)-net over F₉	[i]
8	Digital (87, 108, 5941)-net over F₉	[i]
9	(87, 108, 5943)-net in base 9	[i]