MinT - Information on Result #1179534

Information on Result #1179534

Digital (16, 20, 262147)-net over F₈, using net defined by OOA based on linear OOA(8²⁰, 262147, F₈, 4, 4) (dual of [(262147, 4), 1048568, 5]-NRT-code), using

appending kth column [i] based on linear OOA(8²⁰, 262147, F₈, 3, 4) (dual of [(262147, 3), 786421, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(8²⁰, 524294, F₈, 4) (dual of [524294, 524274, 5]-code), using
  - trace code [i] based on linear OA(64¹⁰, 262147, F₆₄, 4) (dual of [262147, 262137, 5]-code), using
    - constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
      1. linear OA(64¹⁰, 262144, F₆₄, 4) (dual of [262144, 262134, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      2. linear OA(64⁷, 262144, F₆₄, 3) (dual of [262144, 262137, 4]-code or 262144-cap in PG(6,64)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
      3. linear OA(64⁰, 3, F₆₄, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 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 (17, 21, 262147)-net over F₈	[i]	Net Duplication
2	Digital (70, 78, 4456447)-net over F₈	[i]	(u,Â u+v)-Construction for Nets
3	Digital (77, 86, 4456447)-net over F₈	[i]	(u,Â u+v)-Construction for Nets
4	Digital (151, 164, 5854565)-net over F₈	[i]	Generalized (u,Â u+v)-Construction for Nets
5	Digital (152, 165, 5854621)-net over F₈	[i]
6	Digital (144, 156, 5854565)-net over F₈	[i]
7	Digital (145, 157, 5854621)-net over F₈	[i]
8	Digital (149, 162, 5854556)-net over F₈	[i]
9	Digital (150, 163, 5854612)-net over F₈	[i]
10	Digital (151, 164, 5854755)-net over F₈	[i]
11	Digital (152, 165, 5855242)-net over F₈	[i]
12	Digital (142, 154, 5854556)-net over F₈	[i]
13	Digital (143, 155, 5854612)-net over F₈	[i]
14	Digital (144, 156, 5854755)-net over F₈	[i]
15	Digital (145, 157, 5855242)-net over F₈	[i]
16	Digital (146, 159, 5854547)-net over F₈	[i]
17	Digital (139, 151, 5854547)-net over F₈	[i]