MinT - Information on Result #1184354

Information on Result #1184354

Digital (94, 111, 7382)-net over F₃, using net defined by OOA based on linear OOA(3¹¹¹, 7382, F₃, 17, 17) (dual of [(7382, 17), 125383, 18]-NRT-code), using

OOA 8-folding and stacking with additional row [i] based on linear OA(3¹¹¹, 59057, F₃, 17) (dual of [59057, 58946, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹¹¹, 59059, F₃, 17) (dual of [59059, 58948, 18]-code), using
  - constructionÂ X applied to C_e(16) âŠ‚ C_e(15) [i] based on
    1. linear OA(3¹¹¹, 59049, F₃, 17) (dual of [59049, 58938, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    2. linear OA(3¹⁰¹, 59049, F₃, 16) (dual of [59049, 58948, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
    3. linear OA(3⁰, 10, F₃, 0) (dual of [10, 10, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 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 (95, 112, 7382)-net over F₃	[i]	Net Duplication
2	Digital (96, 113, 7382)-net over F₃	[i]
3	Digital (97, 114, 7382)-net over F₃	[i]
4	Digital (102, 119, 7386)-net over F₃	[i]	(u,Â u+v)-Construction for Nets
5	Digital (103, 120, 7389)-net over F₃	[i]
6	Digital (104, 121, 7390)-net over F₃	[i]